Two-stage fourth-order gas kinetic solver-based compact subcell finite volume method for compressible flows on triangular meshes
Two-stage fourth-order gas kinetic solver-based compact subcell finite volume method for compressible flows on triangular meshes
复制标题
基于两级四阶气体动力学求解器的三角形网格上可压缩流动的紧凑子单元有限体积法
作者：
Chao Zhang;Qibing Li;Peng Song;Jiequan Li
为了满足复杂几何形状和高分辨率小尺度流动结构的要求，将气体动力学求解器（GKS）与子单元技术相结合，提出了一种求解（非结构化）三角形网格上可压缩流动的两级四阶子单元有限体积（SCFV）方法，以提高计算的紧凑性和效率。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积（cv），并仅选择面相邻的细胞进行高阶紧凑重建，有效地实现了紧凑性。由于主单元中的一组CV共享相同的重构，因此它比传统的FV-GKS效率更高，传统的FV-GKS需要单独重构每个CV的解多项式。与单级三阶SCFV-GKS不同，两级四阶时间离散化可以显著提高精度和效率，只需一个二阶气体分布函数，简化了通量函数的构建，降低了计算成本。对于粘性流动，不需要用GKS计算粘性项。与第四阶段龙格-库塔方法相比，节省了一半的阶段来实现四阶时间精度，这也有助于提高效率。因此，将SCFV方法与两级气体动力学通量相结合，提出了一种紧凑、高效、鲁棒的高阶方法。通过几个基准案例的测试，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 on (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 in a main cell share the same reconstruction, it is more efficient than traditional FV-GKS, where the solution polynomial on 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.