Techniques for improving monotonicity in a fourth-order finite-volume algorithm solving shocks and detonations
Techniques for improving monotonicity in a fourth-order finite-volume algorithm solving shocks and detonations
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DOI：
10.1016/j.jcp.2020.109515
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
D. Owens;Xinfeng Gao;S. Guzik
中科院分区：
文献类型：
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作者：
D. Owens;Xinfeng Gao;S. Guzik
提出了减少四阶有限体积算法中的数值振荡的技术，该算法用于求解具有强不连续性的热完美反应流体流动，例如冲击波或爆震波。这些额外的机制已被证明是必要的多物种流解决在四阶精度，并有助于边界附近的强不连续性的解决方案的变化。在那里，振荡可以形成由于强梯度的流动，并可能进一步加强了数值程序引入治疗的热完美的热力学系统和物质的质量分数的物理约束。新技术的目的是尊重保守性的基本算法，保持四阶精度的解决方案在光滑流的区域，并配合高阶分段抛物方法限制器。广泛的数值试验，从多组分混合流反应流与爆震，进行验证，新技术满足设计标准，同时有效地抑制振荡。所提出的技术应用于解决Shu-Osher和双马赫反射问题和一组斜爆轰波问题。实验结果证明了该算法的有效性和鲁棒性。
Techniques are proposed to reduce numerical oscillations in a fourth-order, finite-volume algorithm for solving thermally-perfect, reacting fluid flows with strong discontinuities, such as shock or detonation waves. These additional mechanisms have proven necessary for multispecies flows solved at fourth-order accuracy, and contribute towards bounding the variation of the solution in the vicinity of strong discontinuities. There, oscillations can form due to strong gradients in the flow and may be further intensified by numerical procedures introduced to treat the thermally-perfect thermodynamic system and physical constraints on species mass fractions. The new techniques are designed to respect the conservative property of the base algorithm, retain fourth-order accuracy of the solution in regions of smooth flow, and cooperate with the high-order piecewise parabolic method limiter. Extensive numerical tests, ranging from multispecies mixing flows to reacting flows with detonations, are performed to verify that the new techniques meet the design criteria while effectively suppressing oscillations. The proposed techniques are applied to solve the Shu-Osher and double Mach reflection problems and a set of oblique detonation wave problems. The results demonstrate the effectiveness and robustness of the algorithm.