A Stable Adaptive Numerical Scheme for Hyperbolic Conservation Laws.
Abstract
Certain problems in gas dynamics, oil reservoir simulation and other fields can be modeled by hyperbolic conservation laws, a class of partial differential equations. The solutions of such problems are typically made up of smooth surfaces separated by discontinuities, or shocks. Usually, less information is needed to specify the solution in the smooth regions than in the shock regions. In this paper the author introduces a stable finite-difference scheme for conservation laws that incorporates a time-varying, nonuniform computational mesh. At any given time, his mesh selection algorithm chooses a mesh based on the approximation calculated up to the time. The algorithm uses knowledge of a solution's structure to reduce the number of meshpoints in the regions where the solution is smooth. This reduces the method's computational complexity while maintaining full accuracy. He proves that his method is stable for the complete nonlinear problem, and that it converges for linear problems. Given are examples where the method is asymptotically faster than previous ones.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1983
- Accession Number
- ADA130512
Entities
People
- Bradley J. Lucier
Organizations
- University of Wisconsin–Madison