Application of WENO-Schemes for Modelling Shock-Wave Processes

This paper analyzes weighted essentially non-oscillatory (WENO)-schemes for the solution of one-dimensional Euler equations with a Mie−Grüneisen type of equation of state. The least dissipative and oscillatory modifications of WENO-schemes in characteristic variables with a monotonicity-preserving (MP) limiter are presented. A modified scheme, MP-WENO-SM, is developed, demonstrating the smallest amplitude of oscillations in the solution of the test problems with discontinuous initial data.