# A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

## Abstract

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Laboratory (INL)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1062197

- Report Number(s):
- INL/JOU-13-28296

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Journal Article

- Journal Name:
- Communications in Computational Physics

- Additional Journal Information:
- Journal Volume: 12; Journal Issue: 5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS; least-squares reconstruction; compressible Euler equations; Discontinuous Galerkin methods

### Citation Formats

```
Hong Luo, Luqing Luo, and Robert Nourgaliev.
```*A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids*. United States: N. p., 2012.
Web.

```
Hong Luo, Luqing Luo, & Robert Nourgaliev.
```*A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids*. United States.

```
Hong Luo, Luqing Luo, and Robert Nourgaliev. Thu .
"A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids". United States.
```

```
@article{osti_1062197,
```

title = {A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids},

author = {Hong Luo and Luqing Luo and Robert Nourgaliev},

abstractNote = {A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.},

doi = {},

journal = {Communications in Computational Physics},

number = 5,

volume = 12,

place = {United States},

year = {2012},

month = {11}

}