标题： 一种用于加速低雷诺数不可压缩流模拟的粗网格增量压力投影方法 显示英文标题

标题： A coarse-grid incremental pressure-projection method for accelerating low Reynolds-number incompressible flow simulations

摘要： 粗网格投影（CGP）多重网格技术适用于包含至少一个解耦的线性椭圆方程的方程组。 在CGP中，相对于其他方程，线性椭圆方程是在一个更粗的网格上求解的，从而节省了计算时间和复杂性。 CGP最重要的应用之一是当使用压力修正方案来获得纳维-斯托克斯方程的数值解时。 在这种情况下存在一个椭圆压力泊松方程。 根据所使用的压力修正方案，CGP方法及其在加速率和精度水平方面的性能会有所不同。 CGP框架已经为非增量压力投影技术建立。 在本文中，我们首次将CGP方法应用于增量压力修正方案。 考虑了增量算法的标准形式和旋转形式。 研究了速度狄利克雷边界条件和自然齐次边界条件在规则和不规则域中以及结构化和非结构化三角形有限元网格中的影响。 $L^2$范数表明，速度场和压力场的精度级别在最多三层粗化的情况下得到保持。 对于所研究的测试案例，加速因子范围从1.248到102.715。 显示英文摘要

摘要： Coarse grid projection (CGP) multigrid techniques are applicable to sets of equations that include at least one decoupled linear elliptic equation. In CGP, the linear elliptic equation is solved on a coarsened grid compared to the other equations, leading to savings in computations time and complexity. One of the most important applications of CGP is when a pressure correction scheme is used to obtain a numerical solution to the Navier-Stokes equations. In that case there is an elliptic pressure Poisson equation. Depending on the pressure correction scheme used, the CGP method and its performance in terms of acceleration rate and accuracy level vary. The CGP framework has been established for non-incremental pressure projection techniques. In this article, we apply CGP methodology for the first time to incremental pressure correction schemes. Both standard and rotational forms of the incremental algorithms are considered. The influence of velocity Dirichlet and natural homogenous boundary conditions in regular and irregular domains with structured and unstructured triangular finite element meshes is investigated. $L^2$ norms demonstrate that the level of accuracy of the velocity and the pressure fields is preserved for up to three levels of coarsening. For the test cases investigated, the speedup factors range from 1.248 to 102.715.