High-order methods for hypersonic flows with strong shocks and real chemistry
High-order methods for hypersonic flows with strong shocks and real chemistry
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DOI：
10.1016/j.jcp.2023.112310
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
A. Peyvan;K. Shukla;Jesse Chan;G. Karniadakis
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文献类型：
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作者：
A. Peyvan;K. Shukla;Jesse Chan;G. Karniadakis
我们比较了谱差（SD）、通量重建（FR）、熵稳定间断伽辽金谱元法（ES-DGSEM）、模态间断伽辽金法和WENO等高阶方法，以选择模拟高超声速流强激波特性的最佳候选方法。我们考虑了几个基准，包括勒布朗和修改后的冲击密度波相互作用问题，这些问题需要强大的稳定性和正性保持特性才能成功实现流动。我们还使用欧拉方程中引入的化学反应源项，通过简化化学来模拟三物种 Sod 问题。 ES-DGSEM 方案表现出最高的稳定性、可忽略的数值振荡，并且在解析具有强冲击波的反应流态时需要最少的计算工作。因此，我们通过推导五种气体模型的一组新的两点熵保守通量，将 ES-DGSEM 扩展到高超声速欧拉方程。在本文中，高超声速欧拉方程是指使用刚性转子谐波振荡器模型计算内能和热力学性质的多物种欧拉方程。通过将高阶熵保守通量与使用 HLLC 黎曼求解器构建的低阶有限体积通量混合，可以实现捕获强冲击波的稳定性。使用非平衡化学 Sod 问题验证了高超声速欧拉求解器。为此，我们采用 Mutation++ 库来计算反应源项、热力学性质和传递系数。我们还研究了真实化学与理想化学的影响，结果表明理想化学假设在高温下失败，因此必须采用真实化学来进行准确预测。最后，我们考虑粘性高超声速流问题来验证 Mutation++ 库确定的输运系数和反应源项。
We compare high-order methods including spectral difference (SD), flux reconstruction (FR), the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal discontinuous Galerkin methods, and WENO to select the best candidate to simulate strong shock waves characteristic of hypersonic flows. We consider several benchmarks, including the Leblanc and modified shock-density wave interaction problems that require robust stabilization and positivity-preserving properties for a successful flow realization. We also perform simulations of the three-species Sod problem with simplified chemistry with the chemical reaction source terms introduced in the Euler equations. The ES-DGSEM scheme exhibits the highest stability, negligible numerical oscillations, and requires the least computational effort in resolving reactive flow regimes with strong shock waves. Therefore, we extend the ES-DGSEM to hypersonic Euler equations by deriving a new set of two-point entropy conservative fluxes for a five-species gas model. In this paper, hypersonic Euler equations refer to the multi-species Euler equations for which the internal energy and thermodynamic properties are computed using the Rigid-Rotor Harmonic-Oscillator model. Stabilization for capturing strong shock waves occurs by blending high-order entropy conservative fluxes with low-order finite volume fluxes constructed using the HLLC Riemann solver. The hypersonic Euler solver is verified using the non-equilibrium chemistry Sod problem. To this end, we adopt the Mutation++ library to compute the reaction source terms, thermodynamic properties, and transport coefficients. We also investigate the effect of real chemistry versus ideal chemistry, and the results demonstrate that the ideal chemistry assumption fails at high temperatures, hence real chemistry must be employed for accurate predictions. Finally, we consider a viscous hypersonic flow problem to verify the transport coefficients and reaction source terms determined by the Mutation++ library.