High-order consistent SPH with the pressure projection method in 2-D and 3-D
High-order consistent SPH with the pressure projection method in 2-D and 3-D
复制标题
2-D 和 3-D 压力投影法的高阶一致 SPH
DOI：
10.1016/j.jcp.2021.110563
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发表时间：
2021
影响因子：
4.1
通讯作者：
Nasar A
中科院分区：
文献类型：
--
作者：
Nasar A
对于复杂域中的流动，诸如平滑粒子流体动力学 (SPH) 之类的无网格方法比基于网格的方法具有优势，但使用传统形式的 SPH 获得一致的高阶精确解仍有待解决。高阶平滑误差在 SPH 误差中占主导地位，直到越来越精细的分辨率导致低阶离散化误差占主导地位；这与将体积积分离散化为求和有关。本文提出了一种基于修正SPH（MSPH）和修正有限粒子法（FPM）的高阶一致性校正来提高极限离散误差的阶数。新技术是这些方案的任意高阶扩展，其中通过使用平滑核导数的简化版本来降低一致性校正和所需计算的复杂性。所提出的高阶一致 SPH 技术（HOCSPH）以欧拉形式进行测试，与新的高阶 SPH 核函数相结合，旨在提高 SPH 平滑误差的阶数，并且所得到的混合技术最初根据平滑误差收敛，一旦后者占主导地位，则根据 HOCPSH 误差收敛。与具有二阶平滑精度核函数的 HOCSPH 相比，初始高阶收敛降低了使用混合 HOCSPH 实现更高精度所需的计算量。然而，对于高度不规则的分布，发现使用具有二阶平滑精度的内核提供了更一致的收敛特性。使用新的 HOCSPH 技术结合压力投影方法对许多流动进行了 2D 和 3D 模拟，结果表明该方法是准确的并且能够模拟高度复杂的流动模式。确定了与压力-速度搭配相关的投影方法稳定性的一些问题，并提出了几种补救措施。虽然对本文的测试用例有效，但这些补救措施在这种情况下是新的，需要在未来的研究中进一步关注以进行推广。
Mesh-free methods such a smoothed particle hydrodynamics (SPH) have advantages over mesh-based methods for flow in complex domains but attaining consistent high-order accurate solutions with the conventional form of SPH has yet to be resolved. The high-order smoothing error dominates the SPH error until increasingly fine resolutions cause the low-order discretisation error to dominate; this is related to discretising a volume integral into a summation. In this paper, a high-order consistency correction based on modified SPH (MSPH) and the modified finite particle method (FPM) is proposed for improving the order of the limiting discretisation error. The new technique is an arbitrarily high-order extension of these schemes where the complexity of the consistency correction and the required computations are reduced by using simplified versions of the smoothing kernel derivatives. Tested in Eulerian form, the proposed high-order consistent SPH technique (HOCSPH) is combined with new high-order SPH kernel functions, designed to improve the order of the SPH smoothing error, and the resulting hybrid technique is shown to converge according to the smoothing error initially before converging according to the HOCPSH error once the latter becomes dominant. The initial high-order convergence lowers the computational effort required to achieve higher accuracy with hybrid HOCSPH in comparison to HOCSPH with second-order smoothing accuracy kernel functions. However, for highly irregular distributions it is found that the use of kernels with second-order smoothing accuracy provides more consistent convergence properties. A number of flows are simulated in 2-D and 3-D using the new HOCSPH technique in combination with the pressure projection method, and the results show that the method is accurate and able to model highly complex flow patterns. Some issues with stability of the projection method related to pressure–velocity collocation are identified, and several remedies are proposed. While effective for the test cases herein, these remedies are new in this context and require further attention for generalisation in future studies.