Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes
Two-stage Fourth-order Gas Kinetic Solver-based Compact Subcell Finite Volume Method for Compressible Flows over Triangular Meshes
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DOI：
10.1063/5.0073010
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Chao Zhang;Qibing Li;Peng Song;Jiequan Li
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文献类型：
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作者：
Chao Zhang;Qibing Li;Peng Song;Jiequan Li
为了满足小尺度流动结构的复杂几何形状和高分辨率的要求，将气体动力学求解器(GKS)和亚格子技术相结合，提出了一种两级四阶亚格子有限体积(ScFv)方法，用于求解(非结构)三角形网格上的可压缩流动，以提高紧凑性和计算效率。与基于四阶GKS的传统有限体积(FV)方法相比，该方法通过将每个细胞细分为一组子细胞或控制体(CV)，并只选择与人脸相邻的细胞进行高阶紧致重建，从而有效地实现了紧致。由于一组CV共享一个解多项式，因此重建效率比传统的FV-GKS更高，传统的FV-GKS需要单独重建每个CV。与单级三阶SCFv-GKS不同，两级四阶时间离散化显著提高了精度和效率，只需要一个二阶气体分布函数，简化了通量函数的构造，降低了计算量。对于粘性流动，不需要用GKS计算粘性项。与四阶Runge-Kutta方法相比，为了达到四阶时间精度，节省了一半的阶段，这也有助于提高效率。因此，将SCFv方法与两级气体动能通量相结合，提出了一种新的紧凑、高效、稳健性强的高阶方法。通过几个基准算例验证了该方法在可压缩流动模拟中的性能。
To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourth-order subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible flows over (unstructured) triangular meshes was developed to improve the compactness and efficiency. Compared to the fourth-order GKS-based traditional finite volume (FV) method, the proposed method realizes compactness effectively by subdividing each cell into a set of subcells or control volumes (CVs) and selecting only face-neighboring cells for high-order compact reconstruction. Because a set of CVs share a solution polynomial, the reconstruction is more efficient than that for traditional FV-GKS, where each CV needs to be separately reconstructed. Unlike in the single-stage third-order SCFV-GKS, both accuracy and efficiency are improved significantly by two-stage fourth-order temporal discretization, for which only a second-order gas distribution function is needed to simplify the construction of the flux function and reduce computational costs. For viscous flows, it is not necessary to compute the viscous term with GKS. Compared to the fourth-stage Runge--Kutta method, one half of the stage is saved for achieving fourth-order time accuracy, which also helps to improve the efficiency. Therefore, a new high-order method with compactness, efficiency, and robustness is proposed by combining the SCFV method with the two-stage gas-kinetic flux. Several benchmark cases were tested to demonstrate the performance of the method in compressible flow simulations.