Multi-Dimensional Asymptotically Stable Finite Difference Schemes for the Advection-Diffusion Equation.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1996
- Accession Number
- ADA314204
Entities
People
- Adi Ditkowski
- Saul Abarbanel