Name
Abstract | ||
|---|---|---|
Second and higher order numerical approximations of conservation laws for vector fields call for the use of limiting techniques based on generalized monotonicity criteria. In this paper, we introduce a family of directional vertex-based slope limiters for tensor-valued gradients of formally second-order accurate piecewise-linear discontinuous Galerkin (DG) discretizations. The proposed methodology enforces local maximum principles for scalar products corresponding to projections of a vector field onto the unit vectors of a frame-invariant orthogonal basis. In particular, we consider anisotropic limiters based on singular value decompositions and the Gram-Schmidt orthogonalization procedure. The proposed extension to hyperbolic systems features a sequential limiting strategy and a global invariant domain fix. The pros and cons of different approaches to vector limiting are illustrated by the results of numerical studies for the two-dimensional shallow water equations and for the Euler equations of gas dynamics. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.jcp.2019.01.032 | Journal of Computational Physics |
Keywords | Field | DocType |
Hyperbolic conservation laws,Discontinuous Galerkin methods,Vector limiters,Objectivity,Shallow water equations,Euler equations | Discontinuous Galerkin method,Vector field,Mathematical analysis,Direction vector,Orthogonal basis,Euler equations,Orthogonalization,Mathematics,Shallow water equations,Unit vector | Journal |
Volume | ISSN | Citations |
384 | 0021-9991 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hennes Hajduk | 1 | 0 | 0.68 |
| Dmitri Kuzmin | 2 | 167 | 23.90 |
| Vadym Aizinger | 3 | 35 | 8.24 |