论文标题
基于Vanka的参数 - 刺激性多机放松，用于Stokes-Darcy Brinkman问题
A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems
论文作者
论文摘要
我们提出了一个块结构的多族弛豫方案，用于求解由标记和细胞方案离散的Stokes-Darcy Brinkman方程。基于元素的添加剂Vanka平滑剂用于求解相应的Laplacian操作员。使用局部傅立叶分析，我们为添加剂Vanka更平滑的模板提供了一个最佳的平滑因子，用于基于Vanka的Braess-Sarazin弛豫，用于Stokes-Darcy Brinkman方程。尽管最佳阻尼参数取决于网格大小和物理参数，但它非常接近一个。提出了两个网格和V（1,1）循环的数值结果，这些结果表明提出的放松方案的效率很高及其对物理参数和网状尺寸的鲁棒性。使用等于一个的阻尼参数几乎与较低计算开销处的最佳阻尼参数的结果几乎相同。
We propose a block-structured multigrid relaxation scheme for solving the Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An element-based additive Vanka smoother is used to solve the corresponding shifted Laplacian operator. Using local Fourier analysis, we present the stencil for the additive Vanka smoother and derive an optimal smoothing factor for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman equations. Although the optimal damping parameter is dependent on meshsize and physical parameter, it is very close to one. Numerical results of two-grid and V(1,1)-cycle are presented, which show high efficiency of the proposed relaxation scheme and its robustness to physical parameters and the meshsize. Using a damping parameter equal to one gives almost the same results as these for the optimal damping parameter at a lower computational overhead.
