Hybrid monotonicity-preserving piecewise parabolic method for compressible Euler equations. (15th December 2017) - Yu, Yaqun
Highlights: A hybrid scheme for solutions of compressible Euler equations is proposed. Monotonicity preserving is used with a piecewise parabolic method for robustness. Strong robustness with high accuracy and high resolution was obtained. Abstract: In this article, we present a high-accuracy high-resolution hybrid scheme with strong robustness for solutions of compressible Euler equations, particularly those relating to strong discontinuity. The fifth-order monotonicity-preserving (MP5) scheme of Suresh and Huynh has high accuracy; however, its robustness is relatively weak. To improve the robustness and resolution, the MP5 scheme is conjugated with a fourth-order piecewise parabolic method (PPM) in a complementary approach. An adaptive constraint is used to detect which scheme is applied at the current position to guarantee the strong robustness and high accuracy. Through numerical experiments, our hybrid scheme demonstrates a stronger robustness and higher resolution than the traditional scheme and the hybrid scheme MP5-R by He without loss of accuracy.