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Numerical Diffusion
Numerical diffusion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher diffusivity than the true medium. This phenomenon can be particularly egregious when the system should not be diffusive at all, for example an ideal fluid acquiring some spurious viscosity in a numerical model. Explanation In Eulerian simulations, time and space are divided into a discrete grid and the continuous differential equations of motion (such as the Navier–Stokes equation) are discretized into finite-difference equations. The discrete equations are in general more diffusive than the original differential equations, so that the simulated system behaves differently than the intended physical system. The amount and character of the difference depends on the system being simulated and the type of discretization that is used. Most fluid dynamics or magnetohydrodynamic simulations seek to reduce numerical diffusion to the minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent 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-scale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma (physics)
Plasma () is a state of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including the Sun), but also dominating the rarefied intracluster medium and Outer space#Intergalactic space, intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field. The presence of charged particles makes plasma electrically conductive, with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma display, plasma televisions or plasma etching. Depending on temperature and density, a certain number of neutral particles may also be present, in wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Error
In software engineering and mathematics, numerical error is the error in Numerical computation, the numerical computations. Types It can be the combined effect of two kinds of error in a calculation. The first is referred to as Round-off error and is caused by the finite Precision (computer science), precision of computations involving floating-point numbers. The second, usually called Truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation. Measure Floating-point numerical error is often measured in ULP (unit in the last place). See also * Loss of significance * Numerical analysis * Error analysis (mathematics) * Round-off error * Kahan summation algorithm * Numerical sign problem References * ''Accuracy and Stability of Numerical Algorithms'', Nicholas J. Higham, * "Computational Error And Complexity In Science And ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Dispersion
In computational mathematics, numerical dispersion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher dispersivity than the true medium. This phenomenon can be particularly egregious when the system should not be dispersive at all, for example a fluid acquiring some spurious dispersion in a numerical model. It occurs whenever the dispersion relation for the finite difference approximation is nonlinear. For these reasons, it is often seen as a numerical error. Numerical dispersion is often identified, linked and compared with numerical diffusion, another artifact of similar origin. Explanation In simulations, time and space are divided into discrete grids and the continuous differential equations of motion (such as the Navier–Stokes equation) are discretized into finite-difference equations; these discrete equations are in general unidentical to the original differential equations, so the simulated system behaves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Diffusion
False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate Finite difference#central difference, central difference scheme can be used for the convection term, but for grids with cell Peclet number more than 2, the central difference scheme is unstable and the simpler upwind scheme is often used. The resulting error from the upwind differencing scheme has a diffusion-like appearance in two- or three-dimensional co-ordinate systems and is referred as "false diffusion". False-diffusion errors in numerical solutions of convection-diffusion problems, in two- and three-dimensions, arise from the numerical approximations of the convection term in the conservation equations. Over the past 20 years many numerical analysis, numerical techniques have been developed to solve convection-diffusion equations and none are problem-free, but false diffusion is one of the most serious problems a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon Mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedron, polyhedral object's surface. It simplifies Rendering (computer graphics), rendering, as in a wire-frame model. The face (geometry), faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygon, convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygon, concave polygons, or even Polygon with holes, polygons with holes. The study of Polygon (computer graphics), polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes includes Boolean logic (Constructive solid geometry), Subdivision surfaces, smoothing, and Level of detail (computer graphics), simplification. Algorithms also exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Field Models
Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematical space in which each possible state of a physical system is represented by a point also referred to as a "microscopic state" ** Phase space formulation, a formulation of quantum mechanics in phase space *Phase (waves), the position of a point in time (an instant) on a waveform cycle **Instantaneous phase, generalization for both cyclic and non-cyclic phenomena * AC phase, the phase offset between alternating current electric power in multiple conducting wires **Single-phase electric power, distribution of AC electric power in a system where the voltages of the supply vary in unison **Three-phase electric power, a common method of AC electric power generation, transmission, and distribution *Phase problem, the loss of information (the phase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Animation(2)
Animation is a filmmaking technique whereby image, still images are manipulated to create Motion picture, moving images. In traditional animation, images are drawn or painted by hand on cel, transparent celluloid sheets to be photographed and exhibited on film. Animation has been recognised as an artistic medium, specifically within the Entertainment#Industry, entertainment industry. Many animations are either traditional animations or computer animations made with computer-generated imagery (CGI). Stop motion animation, in particular claymation, has continued to exist alongside these other forms. Animation is contrasted with live action, although the two do not exist in isolation. Many moviemakers have produced Live-action animation, films that are a hybrid of the two. As CGI increasingly Photorealism, approximates photographic imagery, filmmakers can easily Compositing, composite 3D animations into their film rather than using practical effects for showy visual effects (VFX). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Resistivity
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Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum (from Latin '' pellere'' "push, drive") is: \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Current Sheet
A current sheet is an electric current that is confined to a surface, rather than being spread through a volume of space. Current sheets feature in magnetohydrodynamics (MHD), a model of electrically conductive fluids: if there is an electric current through part of the volume of such a fluid, magnetic forces tend to expel it from the fluid, compressing the current into thin layers that pass through the volume. The largest occurring current sheet in the Solar System is the so-called heliospheric current sheet, which is about 10,000 km thick, and extends from the Sun and out beyond the orbit of Pluto. In astrophysical plasmas such as the solar corona, current sheets theoretically might have an aspect ratio (breadth divided by thickness) as high as 100,000:1. By contrast, the pages of most books have an aspect ratio close to 2000:1. Because current sheets are so thin in comparison to their size, they are often treated as if they have zero thickness; this is a result of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
