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Immersed Boundary Method
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations (the elastic boundary changes the flow of the fluid and the fluid moves the elastic boundary simultaneously). In the immersed boundary method the fluid is represented in an Eulerian coordinate system and the structure is represented in Lagrangian coordinates. For Newtonian fluids governed by the Navier–Stokes equations, the fluid equations are : \rho \left(\frac + \cdot\nabla\right) = -\nabla p + \mu\, \Delta u(x,t) + f(x,t) and if the flow is incompressible, we have the further condition that : \nabla \cdot u = 0. \, The immersed structures are typically represented as a collection of one-dimensional fibers, denoted by \Gamma . Each fiber can be viewed as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the free-stream flow of the fluid, and the interaction of the fluid ( liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests. CFD is applied to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles S
Charles is a masculine given name predominantly found in English language, English and French language, French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic, Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was ''Churl, Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinisation of names, Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as ''Carolus (other), Carolus''. Some Germanic languages, for example Dutch language, Dutch and German language, German, have retained the word in two separate senses. In the particular case of Dutch, ''Karel'' refers to the given name, whereas the noun ''kerel'' means "a bloke, fellow, man". Etymology The name's etymology is a Common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
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 (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. 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 and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian And Eulerian Coordinates
__NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location. The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newtonian Fluids
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. A fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively. Newtonian fluids are the simplest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express conservation of momentum and conservation of mass for Newtonian fluids. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equations take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta Function
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form acting on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Eulerian Lagrangian Method
In computational fluid dynamics, the Stochastic Eulerian Lagrangian Method (SELM) is an approach to capture essential features of fluid-structure interactions subject to thermal fluctuations while introducing approximations which facilitate analysis and the development of tractable numerical methods. SELM is a hybrid approach utilizing an Eulerian description for the continuum hydrodynamic fields and a Lagrangian description for elastic structures. Thermal fluctuations are introduced through stochastic driving fields. The SELM fluid-structure equations typically used are : \rho \frac = \mu \, \Delta u - \nabla p + \Lambda Upsilon(V - \Gamma)+ \lambda + f_\mathrm(x,t) : m\frac = -\Upsilon(V - \Gamma) - \nabla \Phi + \xi + F_\mathrm : \frac = V. The pressure ''p'' is determined by the incompressibility condition for the fluid : \nabla \cdot u = 0. \, The \Gamma, \Lambda operators couple the Eulerian and Lagrangian degrees of freedom. The X, V denote the composite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokesian Dynamics
Stokesian dynamics is a solution technique for the Langevin equation, which is the relevant form of Newton's 2nd law for a Brownian particle. The method treats the suspended particles in a discrete sense while the continuum approximation remains valid for the surrounding fluid, i.e., the suspended particles are generally assumed to be significantly larger than the molecules of the solvent. The particles then interact through hydrodynamic forces transmitted via the continuum fluid, and when the particle Reynolds number is small, these forces are determined through the linear Stokes equations (hence the name of the method). In addition, the method can also resolve non-hydrodynamic forces, such as Brownian forces, arising from the fluctuating motion of the fluid, and interparticle or external forces. Stokesian Dynamics can thus be applied to a variety of problems, including sedimentation, diffusion and rheology, and it aims to provide the same level of understanding for multiphase parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Of Fluid Method
In computational fluid dynamics, the volume of fluid (VOF) method is a free-surface modelling technique, i.e. a numerical technique for tracking and locating the free surface (or fluid–fluid interface). It belongs to the class of Eulerian methods which are characterized by a mesh that is either stationary or is moving in a certain prescribed manner to accommodate the evolving shape of the interface. As such, VOF is an advection scheme—a numerical recipe that allows the programmer to track the shape and position of the interface, but it is not a standalone flow solving algorithm. The Navier–Stokes equations describing the motion of the flow have to be solved separately. The same applies for all other advection algorithms. History The volume of fluid method is based on earlier Marker-and-cell (MAC) methods. First accounts of what is now known as VOF have been given by Noh & Woodward in 1976, where fraction function C (see below) appeared, although the first publication in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level-set Method
Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the ''Eulerian approach''). Also, the level-set method makes it very easy to follow shapes that change topology, for example, when a shape splits in two, develops holes, or the reverse of these operations. All these make the level-set method a great tool for modeling time-varying objects, like inflation of an airbag, or a drop of oil floating in water. The figure on the right illustrates several important ideas about the level-set method. In the upper-left corner we see a shape; that is, a bounded region with a well-behaved boundary. Below it, the red surface is the graph of a level set function \varphi determining this shape, and the flat blue region r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marker-and-cell Method
The marker-and-cell method is commonly used in computer graphics to discretize functions for fluid and other simulations. It was developed by Francis Harlow and his collaborators at the Los Alamos National Laboratory. See also *Immersed boundary method *Stokesian dynamics *Volume of fluid method *Level-set method Level-set methods (LSM) are a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. The advantage of the level-set model is that one can perform numerical computations involving curves and surfaces on a ... References External linksFluid flow for the rest of us an explanation of fluid simulation (including the MAC grid) Computational fluid dynamics {{fluiddynamics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
