An Implicit Finite Difference Scheme with Preconditioning for Convection Dominated Diffusion Equation
ABSTRACT An implicit finite difference scheme for solving time-dependent convection dominated diffusion equations in two space variables is presented. A one-sided difference approximation is used for the convection terms and a second-order central difference approximation for the diffusion term. The implicit scheme is consistent, unconditionally stable and itpsilas L2 error estimation is optimal. By preconditioning technique of incremental unknowns, the implicit scheme is an efficient one.
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- Water Resources Research 06/1971; 7(3):755-756. DOI:10.1029/WR007i003p00755 · 3.71 Impact Factor
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ABSTRACT: A class of implicit finite element upwind schemes for solving Euler equations is presented. Steady flows with extreme conditions such as high Mach numbers or/and large angles of attack on unstructured meshes can be simulated. Upwind methods are used for the spatial approximation. Higher rates of convergence are obtained by using an implicit scheme relying on a linearization of fluxes and a partial resolution of the systems by a Gauss-Seidel algorithm. The scheme that we get is more efficient and robust than explicit time integration.Journal of Computational Physics 09/1989; 84(1-84):174-206. DOI:10.1016/0021-9991(89)90187-3 · 2.49 Impact Factor