Study of numerical methods for hyperbolic conservation laws with stiff source terms

Technical Report · Tue Mar 01 04:00:00 EST 1988

OSTI ID:5249723

Leveque, R J; Yee, H C

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

• Research Organization: National Aeronautics and Space Administration, Moffett Field, CA (USA). Ames Research Center
• OSTI ID: 5249723
• Report Number(s): N-88-18343; NASA-TM-100075; A-88110; NAS-1.15:100075
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
42 ENGINEERING
420400 -- Engineering-- Heat Transfer & Fluid Flow
ADVECTION
CHEMICAL REACTIONS
CONSERVATION LAWS
FLUID FLOW
GAS FLOW
HYPERSONIC FLOW
KINETICS
MASS TRANSFER
MATHEMATICAL MODELS
MATHEMATICS
NUMERICAL ANALYSIS
REACTION KINETICS