Nonlinearly Stable Compact Schemes for Shock Calculations
Abstract
In this paper we discuss the applications of high order compact finite difference methods for shock calculations. The main idea is the definition of a local mean which serves as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while keeping the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total variation stable in one space dimension and maximum norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. The idea in this paper can also be applied to other implicit schemes such as the continuous Galerkin finite element methods. .
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1992
- Accession Number
- ADA253438
Entities
People
- Bernardo Cockburn
- Chi-Wang Shu