Accession Number : ADA314204

Title :   Multi-Dimensional Asymptotically Stable Finite Difference Schemes for the Advection-Diffusion Equation.

Descriptive Note : Contract rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Abarbanel, Saul ; Ditkowski, Adi

PDF Url : ADA314204

Report Date : JUL 1996

Pagination or Media Count : 37

Abstract : An algorithm is presented which solves the multi-dimensional advection-diffusion equation on complex shapes to 2nd-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions, fall. It gives accurate, non-oscillatory results even when boundary layers are not resolved.

Descriptors :   *ALGORITHMS, *FINITE DIFFERENCE THEORY, *PARTIAL DIFFERENTIAL EQUATIONS, MATHEMATICAL MODELS, TIME DEPENDENCE, MATRICES(MATHEMATICS), SHOCK WAVES, ACCURACY, BOUNDARY LAYER, COMPUTATIONAL FLUID DYNAMICS, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, NUMERICAL INTEGRATION, BOUNDARY VALUE PROBLEMS, OPERATORS(MATHEMATICS), REYNOLDS NUMBER, ASYMPTOTIC NORMALITY.

Subject Categories : Operations Research
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE