# A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

## Abstract

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture inmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 936486

- Report Number(s):
- UCRL-JRNL-219484

Journal ID: ISSN 0021-9991; JCTPAH; TRN: US200818%%823

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics, vol. 223, N/A, April 1, 2007, pp. 262-297

- Additional Journal Information:
- Journal Volume: 223; Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS; ACCURACY; DIMENSIONS; GASES; GEOMETRY; MIXTURES; RESOLUTION

### Citation Formats

```
Banks, J W, Schwendeman, D W, Kapila, A K, and Henshaw, W D.
```*A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids*. United States: N. p., 2006.
Web.

```
Banks, J W, Schwendeman, D W, Kapila, A K, & Henshaw, W D.
```*A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids*. United States.

```
Banks, J W, Schwendeman, D W, Kapila, A K, and Henshaw, W D. Mon .
"A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids". United States. https://www.osti.gov/servlets/purl/936486.
```

```
@article{osti_936486,
```

title = {A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids},

author = {Banks, J W and Schwendeman, D W and Kapila, A K and Henshaw, W D},

abstractNote = {A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.},

doi = {},

journal = {Journal of Computational Physics, vol. 223, N/A, April 1, 2007, pp. 262-297},

issn = {0021-9991},

number = ,

volume = 223,

place = {United States},

year = {2006},

month = {2}

}