An artificial diffusivity discontinuous Galerkin scheme for discontinuous flows

In this paper a discontinuous Galerkin (DG) scheme based on artificial diffusivity is developed for discontinuous flows. The artificial diffusivity model takes the formulation in [Kawai S, Lele SK. Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes. J Comput Phys 2008; 227: 9498-526], and to compute the high-order derivatives therein with relatively low order DG schemes (less than fifth order), a novel method which is feasible for unstructured grids is proposed, which incorporates a filter into the differentiation process. Convergence tests show that the computed 1st, 2nd and 3rd derivatives using the proposed method are able to achieve second order accuracy for one- and two-dimensional cases. Several typical test cases are simulated to assess the ability of the artificial diffusivity DG scheme in terms of accuracy and stability. (C) 2013 Elsevier Ltd. All rights reserved.