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This article describes how to use a computer to calculate an approximate numerical solution of the discretized 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 ...
Finite volume method (FVM) is a numerical method. FVM in computational fluid dynamics is used to solve the partial differential equation which arises from the physical conservation law by using discretisation. Convection is always followed by diffusion and hence where convection is considered we have to consider combine effect of convection and ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The hybrid difference scheme [1] [2] is a method used in the numerical solution for convection–diffusion problems. It was introduced by Spalding (1970). It is a combination of central difference scheme and upwind difference scheme as it exploits the favorable properties of both of these schemes. [3] [4]
The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less than −2
The methods used for solving two dimensional Diffusion problems are similar to those used for one dimensional problems. The general equation for steady diffusion can be easily derived from the general transport equation for property Φ by deleting transient and convective terms [1]
Upwind differencing scheme for convection — first-order scheme for convection–diffusion problems; Lax–Wendroff theorem — conservative scheme for hyperbolic system of conservation laws converges to the weak solution; Alternating direction implicit method (ADI) — update using the flow in x-direction and then using flow in y-direction
Convection–diffusion equation. Double diffusive convection; Davey–Stewartson equation; Euler–Tricomi equation; Falkner–Skan boundary layer; Gardner equation in hydrodynamics; General equation of heat transfer; Geophysical fluid dynamics. Potential vorticity; Quasi-geostrophic equations; Shallow water equations; Taylor–Goldstein ...