Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Technical Report · Mon Dec 01 04:00:00 EST 1986

OSTI ID:7019532

Yee, H C; Shinn, J L

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

• Research Organization: National Aeronautics and Space Administration, Moffett Field, CA (USA). Ames Research Center
• OSTI ID: 7019532
• Report Number(s): N-87-14916; NASA-TM-89415; A-87044; NAS-1.15:89415
• Country of Publication: United States
• Language: English

Related Subjects

640400* -- Fluid Physics
657000 -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
CONSERVATION LAWS
DATA
EIGENVALUES
EIGENVECTORS
FINITE DIFFERENCE METHOD
FLUID FLOW
HYPERSONIC FLOW
INFORMATION
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL DATA
NUMERICAL SOLUTION
SHOCK WAVES
THEORETICAL DATA