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Vorticity error based adaptive meshes refinement scheme is developed and employed using spectral element method to simulate flow past object problems. In general, it is hard to predict and enhance meshes effectively in a region where the error is larger in the computational domain by using the conforming mesh method. Employing finer meshes throughout the whole domain leads to lengthy computational time and excessive storage. Therefore, an indicator is used to predict the regions where larger errors exist and mesh refinement is needed. To compare the efficiency of indicators, three kinds of properties are used as mesh refinement indicators, including the synthesis of velocity and pressure estimated error, vorticity estimated error, and estimated error decay rate. Simulations of the cavity flow in Re = 100 and 1000 and the cases of flow past an inclined flat plate in Re = 100 to 1000 are performed with the adaptive mesh method and conforming mesh method. The results show that the adaptive mesh method can provide the same accuracy as that of the conforming mesh method with only 62% of the elements.

Simulation of Vortex Shedding behind a Flat Plate with Vorticity Based Adaptive Spectral Element Method