Abstract
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.
Highlights
Adaptive refinement techniques provide attractive approaches to many classes of problems in computational fluid dynamics
This study shows that the adaptive finite element method can solve problems accurately and make good agreements with solutions obtained by the finite volume method with respect to Strouhal number, drag coefficient, and recirculation length
Other than exploring cases in which mesh refinement is conducted in elements with linear edges, this study addresses the feasibility of the implementation of mesh refinement on curved elements to explore the potential of application on more complex geometries
Summary
Adaptive refinement techniques provide attractive approaches to many classes of problems in computational fluid dynamics. The spectral element method [3] is a high-order weighted residual technique for numerically solving partial differential equations that combines the generality of h-type finite element methods [4, 5] and the rapid convergence rate of ptype spectral methods [6]. The method breaks up complex computational domains into some macrosubdomains called elements upon which trial functions and solutions are represented by Nth order tensor-product orthogonal polynomial expansions to promise high accuracy. Variational projection operators and Gauss numerical quadrature are used in discrete equations which are solved by iteration procedures with tensor-product sum-factorization techniques [7, 8]
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