An artificial diffusivity discontinuous Galerkin scheme for discontinuous flows

Abstract

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.