Improvement of the time marching method in a particle method
Improvement of the time marching method in a particle method
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DOI：
10.1299/transjsme.20-00437
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
T. Matsunaga;S. Koshizuka
中科院分区：
文献类型：
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作者：
T. Matsunaga;S. Koshizuka
本文研究了时变不可压缩流的质点法的计算精度。近年来，针对粒子法的精确空间离散化方法得到了发展。然而，实际的空间收敛速度往往远远低于采用空间离散化方案时给出的前导截断误差的阶数。这表明，相对于空间离散化方案的截断误差，∆t相关误差相当显著。在这种情况下，我们开发了一种新的时间推进方法，通过减少∆t相关误差和改善收敛性来提高计算精度。所提出的时间推进方法与传统方法一样，是基于一阶分数阶方法。然而，与过去的研究相反，对流项被明确地包括在临时速度计算中，作为一种基于欧拉的方法。通过这样做，可以避免由粒子运动引起的∆t相关误差。利用二维Taylor-Green涡旋问题，分别采用二阶和四阶空间离散格式，进行了数值试验。结果表明，传统的时间推进方法的收敛速度远低于空间离散方案的阶数。另一方面，所提出的时间推进方法分别在2阶和4阶空间离散化方案下表现出近似的2阶和4阶收敛性。结果表明，该方法可大大提高计算精度。
This study concerns the computational accuracy of a particle method for a time-dependent incompressible flow. In recent years, accurate spatial discretization schemes have been developed for a particle method. However, the actual convergence rate in space tends to be much lower than the order of the leading truncation error given by an adopted spatial discretization scheme. This suggests that the ∆t-dependent error is comparably significant with respect to the truncation error of the spatial discretization scheme. Under these circumstances, we have developed a new time marching method to improve the computational accuracy by reducing the ∆t-dependent error and improving the convergence property. The proposed time marching method is based on the 1st-order fractional step method, just as the conventional methods. However, as opposed to the past studies, the convection term is explicitly included in the provisional velocity calculation, as an Eulerian-based approach. By doing this, the ∆t-dependent error caused by the particle movement can be avoided. A numerical test has been carried out using the two-dimensional Taylor-Green vortex problem, where 2ndand 4thorder spatial discretization schemes are adopted. As a result, the conventional time marching methods gave much lower convergence rate than the order of the spatial discretization scheme. On the other hand, the proposed time marching method showed approximately 2ndand 4th-order convergence in space with the 2ndand 4th-order spatial discretization schemes, respectively. Therefore, the proposed method is indicated to highly improve the computational accuracy.