一种新的求解对流占优问题的自适应网格细化方法

在均匀网格上求解对流占优问题时,往往会产生数值震荡现象,因此需要局部加密网格来提高解的精度。针对对流占优问题,设计了一种新的自适应网格细化算法。该方法采用流线迎风SUPG(Petrov-Galerkin)格式求解对流占优问题,定义了网格尺寸并通过后验误差估计子修正来指导自适应网格细化,以泡泡型局部网格生成算法BLMG为网格生成器,通过模拟泡泡在区域中的运动得到了高质量的点集。与其他自适应网格细化方法相比,该方法可在同一框架内实现网格的细化和粗化,同时在所有细化层得到了高质量的网格。数值算例结果表明,该方法在求解对流占优问题时具有更高的数值精度和更好的收敛性。

A new adaptive mesh refinement method for convection-dominated problems

Numerical solutions on uniform meshes always exhibit spurious oscillations,especially near the layers when convection dominates the diffusion.To improve the stabilization and accuracy many stabilized finite element methods and adaptive mesh refinement schemes have been proposed.For convection-dominated problems,a new adaptive mesh refinement method based on bubble-type local mesh generation(BLMG)is developed.The streamline upwind Petrov-Galerkin(SUPG)method is used to stabilize the numerical scheme.To refine the mesh,the mesh size is defined and adjusted according to a posteriori error estimator.Finally optimal meshes are generated from the computed mesh size by the BLMG method in which the nodes are viewed as the centers of bubbles and move according to the Newton''s second law of motion.Compared with other mesh generation strategies,the refining and coarsening can be obtained smoothly in the same framework and the updated triangles remain very well shaped at all levels of refinement.Our algorithm is tested on several examples and the numerical results show that the algorithm is robust.