Accession Number : ADA139769

Title :   A Second Order Upwind Flux Method for Hyperbolic Conservation Laws.

Descriptive Note : Final rept.,

Corporate Author : NAVAL OCEAN RESEARCH AND DEVELOPMENT ACTIVITY NSTL STATION MS

Personal Author(s) : McDonald,B E

PDF Url : ADA139769

Report Date : Nov 1983

Pagination or Media Count : 25

Abstract : We present first- and second-order upwind schemes employing a numerically calculated characteristic speed direction and combine them into a simple monotonicity preserving hybrid scheme using the method of flux correction. The first-order scheme is constructed to maintain accuracy at flow reversal points. The hybrid scheme computes a provisional update from the first-order scheme, and then filters the second-order corrections to prevent occurrence of new extrema. We derive analytic solutions for a developing N-wave shock, and compare computed versus analytic results for two different N waves and for a third case involving linear advection of a square wave. Results are given with and without the second-order correction. The second-order results are always superior to first-order results, with the most dramatic difference occurring for the case of linear advection. The results suggest that higher order differences could be substituted in the hybrid scheme to reduce truncation error even further.

Descriptors :   *Shock waves, Wave propagation, Conservation, Mathematical models

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE