A variational reconstructed discontinuous Galerkin method for the steady-state compressible flows on unstructured grids

摘要

In this paper, a third-order reconstructed DG(p(1)p(2)) method based on the variational reconstruction (VR) (Wang et al., 2017 [24]) is developed for simulating the two dimensional steady-state compressible flows on unstructured and hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the variational reconstruction, which exhibits its superior potential in enhancing the level of accuracy compared to the underlying DG method. In this variational rDG(p(1)p(2)) method, the low order degrees of freedom are evolved through the underlying DG(p(1)) method, while the high order degrees of freedom are reconstructed through the variational reconstruction, in which the constitutive relations are built by minimizing the so-called 'cost function'. The cost function is defined by the total interfacial jump integration in the computational domain using the variational method. The large sparse linear system resulted by the variational reconstruction is solved in an efficient way coupled with the temporal discretization for the steady-state simulations. A number of test cases are presented to assess the performance of the new high order variational rDG(p(1)p(2)) method. (C) 2018 Elsevier Inc. All rights reserved.