A simple shock‐capturing technique for high‐order discontinuous Galerkin methods

By Antonio Huerta, E. Casoni, Jaime Peraire. 2012

95 citations recorded by the source corpus.

This article presents a novel shock‐capturing technique for the discontinuous Galerkin (DG) method. The technique is designed for compressible flow problems, which are usually characterized by the presence of strong shocks and discontinuities. The inherent structure of standard DG methods seems to suggest that they are especially adapted to capture shocks because of the numerical fluxes based on suitable approximate Riemann solvers, which, in practice, introduces some stabilization. However, the usual numerical fluxes are not sufficient to stabilize the solution in the presence of shocks for large high‐order elements. Here, a new basis of shape functions is introduced. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization because of numerical fluxes. Large high‐order elements can therefore be used and shocks captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Several numerical examples for transonic and supersonic flows are studied to demonstrate the applicability of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f9097e63625eb1bc7f2441fc1f32822e1b04c284

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Numerical Analysis

Citations in the corpus

A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “It is also very different from the subcell approach forwarded in [54], which smoothly switches between a high order DG scheme and a first order finite volume subcell method based again on an a priori indicator function.”
A moving discontinuous Galerkin finite element method for flows with interfaces (2018, methodology): “FIGURE 16 The computed stagnation enthalpy (22) field corresponding to the grids shown in Figure 14.”