Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations
Abstract
In many time dependent simulations, the solution on most of the domain will be fairly smooth, with discontinuities or highly oscillatory phenomena occurring over only a small fraction of the domain. In problems such as these, a mesh refinement approach can be the most efficient, and often the only practical, solution method. Refined grids with smaller and smaller mesh spacing are placed only where they are needed. Since we are solving a time dependent problem, the regions needing refinement will change, and therefore our grids must adapt with time as well. This thesis presents a method based on the idea of multiple, component girds for the solution of hyperbolic partial differential equations(pde) using explicit finite difference techniques. Based upon Richardson-type estimates of the local truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. In addition, this approach is recursive in that fine grids can themselves contain even finer subgrids. Those grids with finer mesh width is space will also have a smaller mesh width in time, making this is a mesh refinement algorithm in time and space.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1982
- Accession Number
- ADA121307
Entities
People
- Marsha J. Berger
Organizations
- Stanford University