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Hybrid monotonicity-preserving piecewise parabolic method for compressible Euler equations. (English) Zbl 1390.76640

Summary: 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.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q31 Euler equations
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