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High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows

High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows

Year:    2024

Author:    Zhen Gao, Shuang Guo, Bao-Shan Wang, Yaguang Gu

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 781–820

Abstract

Numerical study on compressible two-medium flows has been a hot issue in recent decades. In this study, we design quasi-conservative finite difference alternative weighted essentially non-oscillatory (AWENO) schemes up to the ninth order for the five-equation model with the stiffened gas equation of state. We propose uniformly high-order flux-based bound- and positivity-preserving (BP-P) limiters for the AWENO schemes while preserving the equilibrium solutions simultaneously. Though the BP-P limiters are used, the numerical solutions have the tendency to generate oscillations especially near strong shock and/or rarefaction waves, due to the sudden drastic scale transition of the density, pressure, etc. To resolve fine structures and the transition of different scales, the latest affine-invariant WENO (Ai-WENO) interpolation is adopted and generalized up to the ninth order. In addition, we will systematically derive CFL conditions when the Lax-Friedrichs numerical flux is applied. Moreover, we show the potential of the BP-P limiters for a variant of the five-equation model, usually suggested in finite volume and discontinuous Galerkin methods. For illustration purposes, we adopt the AWENO schemes and derive the corresponding CFL conditions. A variety of one- and two-dimensional test problems illustrate the high order of accuracy, effectiveness, and robustness of the proposed BP-P Ai-AWENO schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0153

Communications in Computational Physics, Vol. 36 (2024), Iss. 3 : pp. 781–820

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    40

Keywords:    Compressible two-medium flow AWENO scheme affine-invariant WENO interpolation bound- and positivity-preserving limiters.

Author Details

Zhen Gao

Shuang Guo

Bao-Shan Wang

Yaguang Gu

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