Algorithms for Hyperbolic Systems and Applications (Paperback)

Recent second and third order finite difference schemes for the computation of weak solution of hyperbolic conservation laws are modified resulting in methods for stiff or non-stiff systems. The modified schemes also fall in the class of central schemes, all of which can be viewed as based on the well-known Lax-Friedrichs (LxF) schemes. The schemes are Riemann-solver free high resolution schemes and therefore not tied to any Eigen- structure of the problem. They can be implemented in a straight forward manner as black-box solvers for general conservation laws and related equations governing the evolution of large gradient phenomena. Their capabilities for both short-time and long-time scheme integrations are assessed. These modified schemes yields results similar to those of splitting, Lax-Wendroff MacCormack, ENO and the Riemann solver schemes. Numerical studies performed on relaxation systems indicate the accuracy and robustness of the modified schemes. In addition, their application to the plasma fluid equations constitutes a novel approach to the numerical integration of such systems.