Boundary Conditions for Suppressing Rapidly Moving Components in Hyperbolic Systems. I.
Abstract
This work is concerned with hyperbolic systems of partial differential equations for which certain of the associated propagation speeds are a great deal larger than the other proposition speeds. Our goal is to find boundary conditions which prevent rapidly moving waves from entering the given spatial domain. Conditions of this type are desirable in certain numerical computations arising in meteorology. In order to find these conditions, we first transform the given system to an approximate diagonal form in such a way that each of the new dependent variables can be identified as a slow, incoming fast, or outgoing fast component of the solution. we then find local boundary conditions which suppress the incoming fast part. Pseudo-differential operators are used throughout the entire process. We consider only linear systems. In Part II of this work (7) these methods are applied in detail to the linearized shallow water equations. The results of numerical tests of various boundary conditions are included in both papers. We also outline a method by which the conditions can be justified analytically. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1982
- Accession Number
- ADA120962
Entities
People
- Robert L. Higdon
Organizations
- University of Wisconsin–Madison