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Volume 36, Issue 3
High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows

Zhen Gao, Shuang Guo, Bao-Shan Wang & Yaguang Gu

Commun. Comput. Phys., 36 (2024), pp. 781-820.

Published online: 2024-10

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  • 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.

  • AMS Subject Headings

76-XX

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COPYRIGHT: © Global Science Press

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@Article{CiCP-36-781, author = {Gao , ZhenGuo , ShuangWang , Bao-Shan and Gu , Yaguang}, title = {High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0153}, url = {http://global-sci.org/intro/article_detail/cicp/23458.html} }
TY - JOUR T1 - High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows AU - Gao , Zhen AU - Guo , Shuang AU - Wang , Bao-Shan AU - Gu , Yaguang JO - Communications in Computational Physics VL - 3 SP - 781 EP - 820 PY - 2024 DA - 2024/10 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0153 UR - https://global-sci.org/intro/article_detail/cicp/23458.html KW - Compressible two-medium flow, AWENO scheme, affine-invariant WENO interpolation, bound- and positivity-preserving limiters. AB -

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.

Gao , ZhenGuo , ShuangWang , Bao-Shan and Gu , Yaguang. (2024). High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows. Communications in Computational Physics. 36 (3). 781-820. doi:10.4208/cicp.OA-2023-0153
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