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Numerical solution of the convection–diffusion equation
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Numerical solution of the convection–diffusion equation : ウィキペディア英語版
Numerical solution of the convection–diffusion equation
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article describes how to use a computer to calculate an approximate numerical solution of the equation, in a time-dependent situation.
In order to be concrete, this article focuses on ''heat flow'', an important example where the convection–diffusion equation applies. However, the same mathematical analysis works equally well to other situations like particle flow.
A general discontinuous finite element formulation is needed.〔“Discontinuous Finite in Fluid Dynamics and Heat transfer” by Ben Q. Li, 2006.〕 The unsteady convection-diffusion problem is considered, at first the known temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection diffusion equation and equation obtained from the differentiation of this equation.
== Equation ==


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