๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Random Projection Method for Hyperbolic Conservation Laws with Stiff Reaction Terms

โœ Scribed by Weizhu Bao; Shi Jin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
616 KB
Volume
163
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

โœฆ Synopsis

We propose a random projection method for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows:

In this problem, the chemical time scales may be orders of magnitude faster than the fluid dynamical time scales, making the problem numerically stiff. A classic spurious numerical phenomenon, the incorrect propagation speeds of discontinuities, occurs in underresolved numerical solutions. We introduce a random projection method for the reaction term by replacing the ignition temperature with a uniformly distributed random variable. The statistical average of this method corrects the spurious shock speed, as will be proved with a scalar model problem and demonstrated by a wide range of numerical examples in inviscid detonation waves in both one and two space dimensions.

๐Ÿ“œ SIMILAR VOLUMES

Numerical Schemes for Hyperbolic Conserv
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms
โœ Shi Jin; C.David Levermore ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 445 KB

was studied by Hsiao and Liu [22] who showed that its solutions exhibit a long-time behavior governed by Hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long-time behavior governed by reduced systems that are parabolic in nature. In this