Preconditioned time-difference methods for solving advective-diffusive systems

Conference · Wed Apr 01 04:00:00 EST 1992

OSTI ID:10155077

Rodrigue, G; Wolitzer, D

Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions that are placed on stable time-step intervals. Stability bounds for explicit time differencing methods on advective-diffusive problems are generally determined by the diffusive part of the problem. These bounds are very small and implicit methods are used instead. The linear systems arising from these implicit methods are generally solved by iterative methods. In this paper we develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods. A stability analysis is performed on a particular version of this method for the diffusion equation. Several computational examples of advective-diffusive problems are solved to demonstrate the increased stability limits.

• Research Organization: Lawrence Livermore National Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 10155077
• Report Number(s): UCRL-JC--110450; CONF-921209--2; ON: DE92014790
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200
BOUNDARY CONDITIONS
BURGERS VECTOR
DIFFERENTIAL EQUATIONS
DIFFUSION
ITERATIVE METHODS
MATHEMATICS AND COMPUTERS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION