A New 3D OpenFoam Solver with Improved Resolution for Hyperbolic Systems on Hybrid Unstructured Grids
A New 3D OpenFoam Solver with Improved Resolution for Hyperbolic Systems on Hybrid Unstructured Grids
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DOI：
10.1016/j.apm.2022.03.022
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发表时间：
2022-04
影响因子：
5
通讯作者：
Lidong Cheng;X. Deng;B. Xie;Yi Jiang;Feng Xiao
中科院分区：
文献类型：
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作者：
Lidong Cheng;X. Deng;B. Xie;Yi Jiang;Feng Xiao
虽然在过去的二十年里，求解双曲型方程组的离散格式的精度和稳健性已经有了很大的提高，但设计一种低耗散、无振荡的方法仍然是一个挑战。特别是将高分辨率非振荡格式推广应用于三维混合非结构网格，不仅算法复杂，而且计算量大。因此，在这项工作中，我们开发了精确、实用和健壮的3D混合非结构OpenFoam求解器，可以广泛应用于工业应用。与现有的基于高次多项式的三维高阶数值解算器不同，该三维格式采用多项式函数和双曲正切函数作为重构函数的两个候选函数。多项式函数采用带有MLP(多维限制过程)斜率限制器的MUSCL格式。采用具有二次曲面表示和高斯求积的多维THINC函数(即THINC/QQ)作为非多项式重建候选函数。利用这些重构候选者，设计了一种在三维非结构网格上显著减小数值耗散的多阶段边界变差减小(BVD)算法，以选择最终的重构函数。然后，通过在开源计算流体动力学(CFD)软件OpenFOAM中实现所提出的方案和算法，开发了用于模拟无粘高速可压缩单相流和两相流的新的求解器。采用基于密度的无粘高速可压缩流动数值模拟方法，构造了EulerEquationFoam-M-TQ-BVD低耗散格式的数值求解程序。为了模拟具有运动物质界面的可压缩多物质流动，基于力学平衡扩散界面模型和MieGrüneisen状态方程，开发了一种名为FiveEquationFoam-M-TQ-BVD的求解程序。通过大范围的基准测试评估了新的求解器的性能，并与现有的三阶WENO(加权本质非振荡)格式等高阶格式进行了比较。新的求解器在临界点、接触不连续性和材料界面上产生卓越的解决方案。此外，与WENO格式相比，该算法在三维混合非结构网格中具有算法简单和更大的灵活性。因此，这项工作为高速可压缩单物质和多物质流动的模拟提供了准确、实用和健壮的数值解算器。
Although the accuracy and the robustness of discretized schemes solving hyperbolic systems have been greatly improved over the last two decades, devising a low-dissipative and non-oscillatory method remains a challenge. Especially, it is algorithmically complicated and computationally expensive to extend and apply high-resolution non-oscillatory schemes to 3D hybrid unstructured grids. Therefore, in this work we develop accurate, practical, and robust 3D hybrid unstructured OpenFoam solvers which can be applied in wide industrial applications. Different from existing 3D high order numerical solvers of which reconstruction schemes are based on polynomials of high degree, the proposed 3D scheme employs a polynomial function and a hyperbolic tangent basis function as two candidates for reconstruction functions. The MUSCL (Monotone Upstream-centered Schemes for Conservation law) scheme with the MLP (Multi-dimensional Limiting Process) slope limiter is adopted as the polynomial function. The multi-dimensional THINC (Tangent of Hyperbola for INterface Capturing) function with quadratic surface representation and Gaussian quadrature, so-called THINC/QQ, is used as the non-polynomial reconstruction candidate. With these reconstruction candidates, a multi-stage boundary variation diminishing (BVD) algorithm which significantly minimizes numerical dissipation is designed on 3D unstructured grids to select the final reconstruction function. With this accurate and robust reconstruction scheme, then we developed new solvers for simulating inviscid high speed compressible single-phase flow and two-phase flow via the implementation of the proposed scheme and algorithm into the open-source computational fluid dynamics (CFD) software, OpenFOAM. The solver with the proposed low-dissipative scheme, named as EulerEquationFoam-M-TQ-BVD, is constructed with the density-based solver for inviscid high speed compressible flow simulations. To simulate compressible multi-material flow with moving material interfaces, a solver named as FiveEquationFoam-M-TQ-BVD is developed based on mechanical-equilibrium diffusive interface model and MieGrüneisen equation of state. The performance of new solvers is evaluated through wide range benchmark tests and are compared with existing high order schemes such as the third-order WENO (Weighted Essentially Non-Oscillatory) scheme. The new solvers produce superior solution across critical points, contact discontinuities and material interfaces. Moreover, in comparison with WENO schemes, the proposed solver enjoys algorithmic simplicity and greater flexibility in 3D hybrid unstructured grids. Thus, this work provides accurate, practical and robust numerical solvers for high speed compressible single- and multi-material flow simulations.