
Accession Number : ADA314204
Title : MultiDimensional Asymptotically Stable Finite Difference Schemes for the AdvectionDiffusion 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 multidimensional advectiondiffusion equation on complex shapes to 2ndorder accuracy and is asymptotically stable in time. This boundederror 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 2D show that the method is effective even where standard schemes, stable by traditional definitions, fall. It gives accurate, nonoscillatory 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