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Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
( computational physics),
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...
,
climatology Climatology (from Ancient Greek, Greek , ''klima'', "place, zone"; and , ''wiktionary:-logia, -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 ...
, chemistry,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditar ...
and
manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a ...
, as well as human systems in
economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analy ...
,
psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...
,
social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...
,
health care Health care or healthcare is the improvement of health via the prevention, diagnosis, treatment, amelioration or cure of disease, illness, injury, and other physical and mental impairments in people. Health care is delivered by health ...
and
engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new
technology Technology is the application of knowledge to reach practical goals in a specifiable and reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in medicine, scie ...
and to estimate the performance of systems too complex for
analytical solution Generally speaking, analytic (from el, ἀναλυτικός, ''analytikos'') refers to the "having the ability to analyze" or "division into elements or principles". Analytic or analytical can also have the following meanings: Chemistry * A ...
s. Computer simulations are realized by running
computer program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer progra ...
s that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around
Kuwait Kuwait (; ar, الكويت ', or ), officially the State of Kuwait ( ar, دولة الكويت '), is a country in Western Asia. It is situated in the northern edge of Eastern Arabia at the tip of the Persian Gulf, bordering Iraq to the no ...
, using multiple supercomputers in the DoD High Performance Computer Modernization Program.
"Researchers stage largest Military Simulation ever"
,
Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, United States. Founded in the 1930s by Caltech researchers, JPL is owned by NASA ...
,
Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...
, December 1997,
Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the ribosome, in 2005; "Largest computational biology simulation mimics life's most essential nanomachine" (news), News Release, Nancy Ambrosiano,
Los Alamos National Laboratory Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, i ...
, Los Alamos, NM, October 2005, webpage:
LANL-Fuse-story7428
.
a complete simulation of the life cycle of ''
Mycoplasma genitalium ''Mycoplasma genitalium'' (''MG'', commonly known as Mgen) is a sexually transmitted, small and pathogenic bacterium that lives on the mucous epithelial cells of the urinary and genital tracts in humans. Medical reports published in 2007 and 2 ...
'' in 2012; and the
Blue Brain The Blue Brain Project is a Swiss brain research initiative that aims to create a digital reconstruction of the mouse brain. The project was founded in May 2005 by the Brain and Mind Institute of ''École Polytechnique Fédérale de Lausanne'' (E ...
project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level."Mission to build a simulated brain begins"
, project of the institute at the
École Polytechnique Fédérale de Lausanne École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine The Seine ( , ) is a river in northern Franc ...
(EPFL), Switzerland, ''
New Scientist ''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publish ...
'', June 2005.
Because of the computational cost of simulation,
computer experiment A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other simi ...
s are used to perform inference such as
uncertainty quantification Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system a ...
.


Simulation versus model

A computer model is the algorithms and equations used to capture the behavior of the system being modeled. By contrast, computer simulation is the actual running of the program that contains these equations or algorithms. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model (or a simulator)", and then either "run the model" or equivalently "run a simulation".


History

Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
in
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
to model the process of nuclear detonation. It was a simulation of 12 hard spheres using a Monte Carlo algorithm. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions are not possible. There are many types of computer simulations; their common feature is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible.


Data preparation

The external data requirements of simulations and models vary widely. For some, the input might be just a few numbers (for example, simulation of a waveform of AC electricity on a wire), while others might require terabytes of information (such as weather and climate models). Input sources also vary widely: * Sensors and other physical devices connected to the model; * Control surfaces used to direct the progress of the simulation in some way; * Current or historical data entered by hand; * Values extracted as a by-product from other processes; * Values output for the purpose by other simulations, models, or processes. Lastly, the time at which data is available varies: * "invariant" data is often built into the model code, either because the value is truly invariant (e.g., the value of π) or because the designers consider the value to be invariant for all cases of interest; * data can be entered into the simulation when it starts up, for example by reading one or more files, or by reading data from a preprocessor; * data can be provided during the simulation run, for example by a sensor network. Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specialized simulation languages. The best-known may be
Simula Simula is the name of two simulation programming languages, Simula I and Simula 67, developed in the 1960s at the Norwegian Computing Center in Oslo, by Ole-Johan Dahl and Kristen Nygaard. Syntactically, it is an approximate superset of AL ...
. There are now many others. Systems that accept data from external sources must be very careful in knowing what they are receiving. While it is easy for computers to read in values from text or binary files, what is much harder is knowing what the
accuracy Accuracy and precision are two measures of '' observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their '' true value'', while ''precision'' is how close the measurements are to each ot ...
(compared to measurement resolution and precision) of the values are. Often they are expressed as "error bars", a minimum and maximum deviation from the value range within which the true value (is expected to) lie. Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an "error analysis" to confirm that values output by the simulation will still be usefully accurate.


Types

Computer models can be classified according to several independent pairs of attributes, including: *
Stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
or deterministic (and as a special case of deterministic, chaotic) – see external links below for examples of stochastic vs. deterministic simulations * Steady-state or dynamic * Continuous or discrete (and as an important special case of discrete, discrete event or DE models) * Dynamic system simulation, e.g. electric systems, hydraulic systems or multi-body mechanical systems (described primarily by DAE:s) or dynamics simulation of field problems, e.g. CFD of FEM simulations (described by PDE:s). * Local or
distributed Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...
. Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes: * Simulations which store their data in regular grids and require only next-neighbor access are called stencil codes. Many CFD applications belong to this category. * If the underlying graph is not a regular grid, the model may belong to the
meshfree method In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, origina ...
class. Equations define the relationships between elements of the modeled system and attempt to find a state in which the system is in equilibrium. Such models are often used in simulating physical systems, as a simpler modeling case before dynamic simulation is attempted. *Dynamic simulations model changes in a system in response to (usually changing) input signals. *''
Stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
'' models use ''
random number generator Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outc ...
s'' to model chance or random events; *A '' discrete event simulation'' (DES) manages events in time. Most computer, logic-test and fault-tree simulations are of this type. In this type of simulation, the simulator maintains a queue of events sorted by the simulated time they should occur. The simulator reads the queue and triggers new events as each event is processed. It is not important to execute the simulation in real time. It is often more important to be able to access the data produced by the simulation and to discover logic defects in the design or the sequence of events. *A ''continuous dynamic simulation'' performs numerical solution of differential-algebraic equations or
differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...
(either partial or
ordinary Ordinary or The Ordinary often refer to: Music * ''Ordinary'' (EP) (2015), by South Korean group Beast * ''Ordinary'' (Every Little Thing album) (2011) * "Ordinary" (Two Door Cinema Club song) (2016) * "Ordinary" (Wayne Brady song) (2008) * ...
). Periodically, the simulation program solves all the equations and uses the numbers to change the state and output of the simulation. Applications include flight simulators, construction and management simulation games, chemical process modeling, and simulations of
electrical circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sour ...
s. Originally, these kinds of simulations were actually implemented on
analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. ...
s, where the differential equations could be represented directly by various electrical components such as
op-amp An operational amplifier (often op amp or opamp) is a DC-coupled high- gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential (relative t ...
s. By the late 1980s, however, most "analog" simulations were run on conventional
digital computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These progra ...
s that emulate the behavior of an analog computer. *A special type of discrete simulation that does not rely on a model with an underlying equation, but can nonetheless be represented formally, is agent-based simulation. In agent-based simulation, the individual entities (such as molecules, cells, trees or consumers) in the model are represented directly (rather than by their density or concentration) and possess an internal state and set of behaviors or rules that determine how the agent's state is updated from one time-step to the next. *
Distributed Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...
models run on a network of interconnected computers, possibly through the
Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a ''internetworking, network of networks'' that consists ...
. Simulations dispersed across multiple host computers like this are often referred to as "distributed simulations". There are several standards for distributed simulation, including Aggregate Level Simulation Protocol (ALSP), Distributed Interactive Simulation (DIS), the High Level Architecture (simulation) (HLA) and the Test and Training Enabling Architecture (TENA).


Visualization

Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation parameters. The use of the matrix format was related to traditional use of the matrix concept in
mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s. However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by computer-generated-imagery (CGI) animation. Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and "see that rain was headed their way") much faster than by scanning tables of rain-cloud
coordinate In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is si ...
s. Such intense graphical displays, which transcended the world of numbers and formulae, sometimes also led to output that lacked a coordinate grid or omitted timestamps, as if straying too far from numeric data displays. Today,
weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th centu ...
models tend to balance the view of moving rain/snow clouds against a map that uses numeric coordinates and numeric timestamps of events. Similarly, CGI computer simulations of
CAT scan A computed tomography scan (CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers ...
s can simulate how a
tumor A neoplasm () is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists ...
might shrink or change during an extended period of medical treatment, presenting the passage of time as a spinning view of the visible human head, as the tumor changes. Other applications of CGI computer simulations are being developed to graphically display large amounts of data, in motion, as changes occur during a simulation run.


In science

Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description: * a numerical simulation of
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...
s that cannot be solved analytically, theories that involve continuous systems such as phenomena in
physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...
,
fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(e.g.,
climate model Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the ...
s, roadway noise models, roadway air dispersion models),
continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such ...
and
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...
fall into this category. * a
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
simulation, typically used for discrete systems where events occur
probabilistic Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
ally and which cannot be described directly with differential equations (this is a ''discrete'' simulation in the above sense). Phenomena in this category include
genetic drift Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and there ...
, biochemical or gene regulatory networks with small numbers of molecules. (see also:
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
). * multiparticle simulation of the response of nanomaterials at multiple scales to an applied force for the purpose of modeling their thermoelastic and thermodynamic properties. Techniques used for such simulations are
Molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
,
Molecular mechanics Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Mo ...
,
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
, and Multiscale Green's function. Specific examples of computer simulations include: * statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibrium
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...
of receiving waters, allowing the gamut of
meteorological Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
data to be input for a specific locale. This technique was developed for thermal pollution forecasting. * agent based simulation has been used effectively in
ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...
, where it is often called "individual based modeling" and is used in situations for which individual variability in the agents cannot be neglected, such as
population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has ...
of
salmon Salmon () is the common name In biology, a common name of a taxon or organism (also known as a vernacular name, English name, colloquial name, country name, popular name, or farmer's name) is a name that is based on the normal language of ...
and
trout Trout are species of freshwater fish belonging to the genera '' Oncorhynchus'', '' Salmo'' and '' Salvelinus'', all of the subfamily Salmoninae of the family Salmonidae. The word ''trout'' is also used as part of the name of some non-sa ...
(most purely mathematical models assume all trout behave identically). * time stepped dynamic model. In hydrology there are several such
hydrology transport model An hydrological transport model is a mathematical model used to simulate the flow of rivers, streams, groundwater movement or drainage front displacement, and calculate water quality parameters. These models generally came into use in the 1960s ...
s such as the SWMM and
DSSAM Model The DSSAM Model (Dynamic Stream Simulation and Assessment Model) is a computer simulation developed for the Truckee River to analyze water quality impacts from land use and wastewater management decisions in the Truckee River Basin. This area in ...
s developed by the U.S. Environmental Protection Agency for river water quality forecasting. * computer simulations have also been used to formally model theories of human cognition and performance, e.g., ACT-R. * computer simulation using molecular modeling for
drug discovery In the fields of medicine, biotechnology and pharmacology, drug discovery is the process by which new candidate medications are discovered. Historically, drugs were discovered by identifying the active ingredient from traditional remedies or by ...
. *computer simulation to model viral infection in mammalian cells. * computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules. *
Computational fluid dynamics Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate t ...
simulations are used to simulate the behaviour of flowing air, water and other fluids. One-, two- and three-dimensional models are used. A one-dimensional model might simulate the effects of
water hammer Hydraulic shock (colloquial: water hammer; fluid hammer) is a pressure surge or wave caused when a fluid in motion, usually a liquid but sometimes also a gas is forced to stop or change direction suddenly; a momentum change. This phenomenon c ...
in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building. * An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows this complex subject to be simplified to down-to-earth presentations of molecular theory. Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows'
World3 The World3 model is a system dynamics model for computer simulation of interactions between population, industrial growth, food production and limits in the ecosystems of the earth. It was originally produced and used by a Club of Rome study that p ...
used in the '' Limits to Growth'', James Lovelock's
Daisyworld Daisyworld, a computer simulation, is a hypothetical world orbiting a star whose radiant energy is slowly increasing or decreasing. It is meant to mimic important elements of the Earth-Sun system, and was introduced by James Lovelock and Andre ...
and Thomas Ray's Tierra. In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method,
replication Replication may refer to: Science * Replication (scientific method), one of the main principles of the scientific method, a.k.a. reproducibility ** Replication (statistics), the repetition of a test or complete experiment ** Replication crisi ...
is an important part of computational modeling


In practical contexts

Computer simulations are used in a wide variety of practical contexts, such as: * analysis of air pollutant dispersion using atmospheric dispersion modeling * design of complex systems such as
aircraft An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. ...
and also
logistics Logistics is generally the detailed organization and implementation of a complex operation. In a general business sense, logistics manages the flow of goods between the point of origin and the point of consumption to meet the requirements of ...
systems. * design of
noise barrier A noise barrier (also called a soundwall, noise wall, sound berm, sound barrier, or acoustical barrier) is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution. Noise barriers are the most effect ...
s to effect roadway noise mitigation * modeling of application performance * flight simulators to train pilots *
weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th centu ...
* forecasting of risk * simulation of electrical circuits * Power system simulation * simulation of other computers is emulation. * forecasting of prices on financial markets (for example Adaptive Modeler) * behavior of structures (such as buildings and industrial parts) under stress and other conditions * design of industrial processes, such as chemical processing plants *
strategic management In the field of management, strategic management involves the formulation and implementation of the major goals and initiatives taken by an organization's managers on behalf of stakeholders, based on consideration of resources and an assessment ...
and
organizational studies Organization studies (also called organization science or organizational studies) is the academic field interested in a ''collective activity, and how it relates to organization, organizing, and management''. It is "the examination of how individua ...
*
reservoir simulation Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the flow of fluids (typically, oil, water, and gas) through porous media. The creation of models of oil fields and the implementation of calc ...
for the petroleum engineering to model the subsurface reservoir * process engineering simulation tools. * robot simulators for the design of robots and robot control algorithms * urban simulation models that simulate dynamic patterns of urban development and responses to urban land use and transportation policies. * traffic engineering to plan or redesign parts of the street network from single junctions over cities to a national highway network to transportation system planning, design and operations. See a more detailed article on Simulation in Transportation. * modeling car crashes to test safety mechanisms in new vehicle models. * crop-soil systems in agriculture, via dedicated software frameworks (e.g. BioMA, OMS3, APSIM) The reliability and the trust people put in computer simulations depends on the
validity Validity or Valid may refer to: Science/mathematics/statistics: * Validity (logic), a property of a logical argument * Scientific: ** Internal validity, the validity of causal inferences within scientific studies, usually based on experiments ...
of the simulation model, therefore
verification and validation Verification and validation (also abbreviated as V&V) are independent procedures that are used together for checking that a product, service, or system meets requirements and specifications and that it fulfills its intended purpose. These ar ...
are of crucial importance in the development of computer simulations. Another important aspect of computer simulations is that of reproducibility of the results, meaning that a simulation model should not provide a different answer for each execution. Although this might seem obvious, this is a special point of attention in stochastic simulations, where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations and
computer games A personal computer game, also known as a PC game or computer game, is a type of video game played on a personal computer (PC) rather than a video game console or arcade machine. Its defining characteristics include: more diverse and user-d ...
. Here a human is part of the simulation and thus influences the outcome in a way that is hard, if not impossible, to reproduce exactly.
Vehicle A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles ( motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles ( trains, trams ...
manufacturers make use of computer simulation to test safety features in new designs. By building a copy of the car in a physics simulation environment, they can save the hundreds of thousands of dollars that would otherwise be required to build and test a unique prototype. Engineers can step through the simulation milliseconds at a time to determine the exact stresses being put upon each section of the prototype.Baase, Sara. A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet. 3. Upper Saddle River: Prentice Hall, 2007. Pages 363–364. .
Computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal ...
can be used to display the results of a computer simulation.
Animations Animation is a method by which still figures are manipulated to appear as moving images. In traditional animation, images are drawn or painted by hand on transparent celluloid sheets to be photographed and exhibited on film. Today, most ani ...
can be used to experience a simulation in real-time, e.g., in training simulations. In some cases animations may also be useful in faster than real-time or even slower than real-time modes. For example, faster than real-time animations can be useful in visualizing the buildup of queues in the simulation of humans evacuating a building. Furthermore, simulation results are often aggregated into static images using various ways of scientific visualization. In debugging, simulating a program execution under test (rather than executing natively) can detect far more errors than the hardware itself can detect and, at the same time, log useful debugging information such as instruction trace, memory alterations and instruction counts. This technique can also detect
buffer overflow In information security and programming, a buffer overflow, or buffer overrun, is an anomaly whereby a program, while writing data to a buffer, overruns the buffer's boundary and overwrites adjacent memory locations. Buffers are areas of memor ...
and similar "hard to detect" errors as well as produce performance information and tuning data.


Pitfalls

Although sometimes ignored in computer simulations, it is very important to perform a sensitivity analysis to ensure that the accuracy of the results is properly understood. For example, the probabilistic risk analysis of factors determining the success of an oilfield exploration program involves combining samples from a variety of statistical distributions using the
Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
. If, for instance, one of the key parameters (e.g., the net ratio of oil-bearing strata) is known to only one significant figure, then the result of the simulation might not be more precise than one significant figure, although it might (misleadingly) be presented as having four significant figures.


See also

* Computational model * Digital Twin * Illustris project * List of computer simulation software * Scene generator *
Simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
*
Simulation hypothesis The simulation hypothesis proposes that all of our existence is a simulated reality, such as a computer simulation. The simulation hypothesis bears a close resemblance to various other skeptical scenarios from throughout the history of philosophy. ...
*
Simulation video game Simulation video games are a diverse super-category of video games, generally designed to closely simulate real world activities. A simulation game attempts to copy various activities from real life in the form of a game for various purposes such ...
* UniverseMachine * Virtual prototyping *
Virtual reality Virtual reality (VR) is a simulated experience that employs pose tracking and 3D near-eye displays to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video games), e ...
* Web-based simulation


References


Further reading

* Young, Joseph and Findley, Michael. 2014. "Computational Modeling to Study Conflicts and Terrorism.
Routledge Handbook of Research Methods in Military Studies
edited by Soeters, Joseph; Shields, Patricia and Rietjens, Sebastiaan. pp. 249–260. New York: Routledge, * R. Frigg and S. Hartmann
Models in Science
Entry in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. E ...
''. *E. Winsber
Simulation in Science
Entry in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. E ...
''. * S. Hartmann
The World as a Process: Simulations in the Natural and Social Sciences
in: R. Hegselmann et al. (eds.), ''Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View'', Theory and Decision Library. Dordrecht: Kluwer 1996, 77–100. * E. Winsberg, ''Science in the Age of Computer Simulation''. Chicago:
University of Chicago Press The University of Chicago Press is the largest and one of the oldest university presses in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including '' The Chicago Manual of Style'' ...
, 2010. * P. Humphreys, ''Extending Ourselves: Computational Science, Empiricism, and Scientific Method''. Oxford:
Oxford University Press Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
, 2004. * * Desa, W. L. H. M., Kamaruddin, S., & Nawawi, M. K. M. (2012). Modeling of Aircraft Composite Parts Using Simulation. Advanced Material Research, 591–593, 557–560.


External links


Guide to the Computer Simulation Oral History Archive 2003-2018
{{Authority control Computational science Virtual reality Alternatives to animal testing Computational fields of study