Applied Partial Differential Equations and Numerical Analysis
Abstract
An hierarchy of uniformly high order accurate essentially non- oscillatory shock capturing algorithms was developed. Some theory and numerical experimentation was done. A correction to the unsteady full potential equation for flows with strong shocks was obtained. This modification inputs the correct entropy jumps at shocks. Numerical experiments on airfoils were sucessfully performed. A new family of paraxial wave approximations was derived and was applied to computational problems in seismology, underwater acoustics and artificial boundaries. Theoretical and experimental results were obtained. The family also included variants of parabolic approximations of scalar wave equations. A method for the computation of highly oscillatory solutions to hyperbolic equations was obtained. A convergence concept which makes analysis possible in the practical situation in which not all frequencies are well resolved is developed. Convergence of an average approximation is established for a general class of methods. Applications to particle methods were also obtained. Keyword: Reports, Abstracts.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1988
- Accession Number
- ADA201749
Entities
People
- Stanley Osher
Organizations
- University of California, Los Angeles