A rational high-order compact ADI method for unsteady convection-diffusion equations

A Fourth-Order Compact Finite Difference Scheme for Solving Unsteady Convection-Diffusion Equations

Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering (Hundsdorfer & Verwer, 2003; Morton, 1996). Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-d...

A CCD-ADI method for unsteady convection-diffusion equations

With a combined compact difference scheme for the spatial discretization and the CrankNicolson scheme for the temporal discretization, respectively, a high-order alternating direction implicit method (ADI) is proposed for solving unsteady two dimensional convectiondiffusion equations. The method is sixth-order accurate in space and second-order accurate in time. The resulting matrix at each ADI...

A high-order Padé ADI method for unsteady convection-diffusion equations

High-order ADI schemes for convection-diffusion equations with mixed derivative terms

We consider new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer [12]. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and sec...

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A stable high order finite difference with a fully implicit time-marching scheme is proposed to solve the two-dimensional unsteady convection diffusion equation with variable coefficients. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. A time-dependent multigrid full approximation storage(FAS) scheme , which is suitab...