Accession Number : ADA130512
Title : A Stable Adaptive Numerical Scheme for Hyperbolic Conservation Laws.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Lucier,Bradley J
PDF Url : ADA130512
Report Date : May 1983
Pagination or Media Count : 44
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.
Descriptors : *Partial differential equations, *Finite difference theory, Operators(Mathematics), Viscosity, Adaptive systems, Problem solving, Mesh, Algorithms, Stability, Computations, Convergence, Nonlinear analysis, Linearity
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE