论文标题
一种用于加速不可压缩的MHD流量模拟的粗网格投影方法
A coarse-grid projection method for accelerating incompressible MHD flow simulations
论文作者
论文摘要
粗网格投影（CGP）是一种多分辨率技术，用于加速与一组非线性进化方程以及硬泊松方程相关的数值计算。在本文中，我们首次使用CGP加快了不可压缩的磁性水力学（MHD）流量模拟。因此，我们在精细网格上求解非线性对流扩散方程，而我们在相应的粗网格上执行电势泊松方程。映射操作员将两个网格连接在一起。压力校正方案用于执行不可压缩性约束。在存在洛伦兹力的情况下，对不可压缩流的研究被选为固定雷诺数但各种stuart数量的基准问题。我们考虑两种不同的情况。首先，我们仅将CGP应用于电势泊松方程。其次，我们也将CGP应用于压力泊松方程。对于第一和第二种情况，此处实现的最大加速因子分别约为3和23。对于两种情况，我们都会检查速度和涡度场的准确性以及升力和阻力系数。通常，通过CGP获得的结果在出色至合理的准确性范围内，并且比我们使用粗网格来离散对流扩散和电势泊松方程时，更加准确。
Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with the stiff Poisson equations. In this article we use CGP for the first time to speed up incompressible magnetohydrodynamics (MHD) flow simulations. Accordingly, we solve the nonlinear advection-diffusion equation on a fine mesh, while we execute the electric potential Poisson equation on the corresponding coarsened mesh. Mapping operators connect two grids together. A pressure correction scheme is used to enforce the incompressibility constrain. The study of incompressible flow past a circular cylinder in the presence of Lorentz force is selected as a benchmark problem with a fixed Reynolds number but various Stuart numbers. We consider two different situations. First, we only apply CGP to the electric potential Poisson equation. Second, we apply CGP to the pressure Poisson equation as well. The maximum speedup factors achieved here are approximately 3 and 23 respectively for the first and second situations. For the both situations we examine the accuracy of velocity and vorticity fields as well as the lift and drag coefficients. In general, the results obtained by CGP are in an excellent to reasonable range of accuracy and are significantly consistently more accurate than when we use coarse grids for the discretization of both the advection-diffusion and electric potential Poisson equations.
