Consideration of artificial compressibility for explicit computational fluid dynamics simulation
Consideration of artificial compressibility for explicit computational fluid dynamics simulation
复制标题
显式计算流体动力学模拟中人工压缩性的考虑
DOI：
10.1016/j.jcp.2021.110524
复制
发表时间：
2021
影响因子：
4.1
通讯作者：
J.
中科院分区：
文献类型：
--
作者：
Nagata;K.;Ikegaya;N.;Tanimoto;J.
本文讨论了人工可压缩方法(ACM)的理论解释，为流体非定常数值模拟提出了一种新的显式方法。该方法采用可压缩连续性和Navier-Stokes方程，理论上支持虚粒子概念，便于用密度代替压力作为主要变量之一。这一新概念证明了假设ACM中的声速作为由网格系统确定的模型参数的理论处理的合理性。更重要的是，本方法以完全显式的方式实现了一组方程的求解，从而避免了求解压力的泊松方程。通过与传统不可压缩方法和雷诺数分别为100、1000和10000的格子-玻尔兹曼方法的二维空腔流动计算结果的比较，验证了新方法的有效性。在定常和非定常条件下，该方法的计算结果与常规数据和参考数据吻合较好，但在雷诺数为10000的情况下，该方法有轻微的数值振荡。因此，数值验证表明，该方法是一种具有坚实理论基础的显式方法，是一种新的高效的仿真框架。
In this paper, we discuss the theoretical interpretation of the artificial compressibility method (ACM) to propose a new explicit method for the unsteady numerical simulation of fluid flow. The proposed method employs the compressible continuity and Navier–Stokes equations, which facilitates the replacement of pressure as one of the major variables with density, theoretically backed by virtual particle concept. This new concept justifies the theoretical treatment assuming the speed of sound in ACM as a model parameter determined by the grid system. More importantly, the present method realizes, in a fully explicit manner, the solving of a set of equations, which prevents the solving of the Poisson equation of pressure. The new method was validated and proven by comparing the results of two-dimensional cavity flow between the proposed method, conventional incompressible method, and the Lattice–Boltzmann method with varying Reynolds numbers (100, 1000, and 10000). The results of the proposed method agree well with conventional and reference data for both steady-state and unsteady-state conditions, although slight numerical oscillations were observed for the proposed method at a Reynolds number of 10000. Thus, the numerical validation assures that the proposed method is an explicit method based on a solid theoretical ground to be a new efficient simulation framework.