Concepts inEnergy-preserving integrators for fluid animation
Integrator
An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus. The integration function is often part of engineering and scientific calculations. Mechanical integrators are used in such applications as metering of water flow or electric power. Electronic analog integrators were the basis of analog computers.
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Fluid
In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. In common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required function if there is gas in it.
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Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity).
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Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow¿the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion).
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Crank¿Nicolson method
In numerical analysis, the Crank¿Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. It is a second-order method in time, it is implicit in time and can be written as an implicit Runge¿Kutta method, and it is numerically stable. The method was developed by John Crank and Phyllis Nicolson in the mid 20th century.
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Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.
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Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is derived from the accuracy of the algorithm. An opposite phenomenon is instability.
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Dissipation
Dissipation is the result of irreversible processes that take place in inhomogeneous systems. These processes produce entropy at a certain rate. The entropy production rate times ambient temperature gives the dissipated power. Important examples of irreversible processes are: heat flow through a thermal resistance, fluid flow through a flow resistance, diffusion (mixing), chemical reactions, and electrical current flow through an electrical resistance (Joule heating).
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