On MaximumPrincipleSatisfying Entropy Scheme for Linear Advection Equation

Abstract:

Mao Dekang et al developed an entropy scheme for computing one dimensional hyperbolic conservation equations, which has a super convergence property and is suitable for long time numerical computation. But the entropy scheme does not satisfy the maximum principle. Overshooting or undershooting may occur in the vicinity of maximum or minimum points. In this work, numerical simulations of one dimensional and two dimensional linear advection equations are carried out. The numerical results show that the proposed scheme does not lead to overshooting or undershooting, moreover, nonphysical oscillations do not occur.

Key words:maximum principle; entropy scheme; linear advection equation