Adaptive anisotropic meshing for steady convection-dominated problems

作者：Nguyen Hoa; Gunzburger Max; Ju Lili^*; Burkardt John

来源：Computer Methods in Applied Mechanics and Engineering, 2009, 198(37-40): 2964-2981.

DOI：10.1016/j.cma.2009.05.001

• Anisotropic mesh generation
• Metric tensor
• Convection-dominated problem
• Stabilized method

Obtaining accurate solutions for convection-diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov-Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.

• 出版日期2009