A positivity‐preserving Lagrangian discontinuous Galerkin scheme with exact Riemann solver for gas‐water compressible flows
A positivity‐preserving Lagrangian discontinuous Galerkin scheme with exact Riemann solver for gas‐water compressible flows
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DOI：
10.1002/fld.5193
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发表时间：
2023-03
影响因子：
1.8
通讯作者：
Wenbin Wu;N. Liu;Chao Huang;Pan Zhang;Moubin Liu
中科院分区：
文献类型：
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作者：
Wenbin Wu;N. Liu;Chao Huang;Pan Zhang;Moubin Liu
在这项研究中，提出了一种新的以单元为中心的拉格朗日不连续伽辽金（DG）方案来模拟气水可压缩流动。两相流由具有理想和硬化气体状态方程的可压缩欧拉方程控制。我们将拉格朗日 DG 格式与精确的气水黎曼求解器相结合来计算数值通量，从而很好地解决了气水可压缩流固有的刚性特征。此外，为了保证高马赫数计算过程中密度和内能的正性，引入保正限制器和强保稳时间积分来保证数值稳定性。通过六个数值算例的测试验证了该方案的准确性、鲁棒性和保正性。可以发现，本方案可以处理涉及大密度比（高达1000）和强冲击的具有挑战性的数值情况。还给出了使用典型 HLLC 通量获得的结果进行比较，并且使用精确黎曼求解器的本方案显示出更高的精度，特别是在气水界面处存在大密度比的情况下。
In this study, a new cell‐centered Lagrangian discontinuous Galerkin (DG) scheme is presented to simulate gas‐water compressible flows. The two‐phase flows are governed by the compressible Euler equation with ideal and stiffened gas equations of state. We integrate the Lagrangian DG scheme with the exact gas‐water Riemann solver for calculating the numerical fluxes so that the inherent stiff features of gas‐water compressible flows are well addressed. Furthermore, in order to guarantee the positivity of the density and internal energy during the high Mach number calculation, the positivity‐preserving limiter and strong stability preserving temporal integral are incorporated to ensure the numerical stability. Six numerical examples are tested to show the accuracy, robustness and positivity‐preserving property of the present scheme. It can be found that the present scheme can handle challenging numerical cases involving large density ratio (up to 1000) and strong shock. The results obtained with the typical HLLC flux are also given for comparison and the present scheme with the exact Riemann solver shows higher accuracy, particularly in the presence of large density ratio at the gas‐water interface.