# Nonreflecting boundary conditions for nonlinear hyperbolic systems

## Abstract

Consider a nonlinear hyperbolic system ..nu../sub t/+A (..nu..) ..nu../sub chi/=0 for chi>0 and t>0. Suppose that the boundary chi=0 has been introduced only in order to limit the size of a computational problem. Suppose also that on physical grounds we know that no waves cross the boundary from the region chi>0. We need a boundary condition at chi=0 which expresses this fact. If our problem has no strong outgoing shocks, we may use the condition that at chi=0 the solution upsilon lies in the manifold generated by the Riemann invariants of the outgoing characteristics. For the equations of gas dynamics with an outflow boundary at chi=0 this condition may be written c/sub upsilon/..gamma..arho/sub t/+cupsilon..gamma..rho/sub t/+arhoS/sub t/=0, where a is the sound speed.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore Laboratory, University of California, Livermore, California 94550

- OSTI Identifier:
- 6143545

- Resource Type:
- Journal Article

- Journal Name:
- J. Comput. Phys.; (United States)

- Additional Journal Information:
- Journal Volume: 30:2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DIFFERENTIAL EQUATIONS; BOUNDARY CONDITIONS; COMPUTER CALCULATIONS; GAS FLOW; NONLINEAR PROBLEMS; SHOCK WAVES; EQUATIONS; FLUID FLOW; 990200* - Mathematics & Computers

### Citation Formats

```
Hedstrom, G.W.
```*Nonreflecting boundary conditions for nonlinear hyperbolic systems*. United States: N. p., 1979.
Web. doi:10.1016/0021-9991(79)90100-1.

```
Hedstrom, G.W.
```*Nonreflecting boundary conditions for nonlinear hyperbolic systems*. United States. doi:10.1016/0021-9991(79)90100-1.

```
Hedstrom, G.W. Thu .
"Nonreflecting boundary conditions for nonlinear hyperbolic systems". United States. doi:10.1016/0021-9991(79)90100-1.
```

```
@article{osti_6143545,
```

title = {Nonreflecting boundary conditions for nonlinear hyperbolic systems},

author = {Hedstrom, G.W.},

abstractNote = {Consider a nonlinear hyperbolic system ..nu../sub t/+A (..nu..) ..nu../sub chi/=0 for chi>0 and t>0. Suppose that the boundary chi=0 has been introduced only in order to limit the size of a computational problem. Suppose also that on physical grounds we know that no waves cross the boundary from the region chi>0. We need a boundary condition at chi=0 which expresses this fact. If our problem has no strong outgoing shocks, we may use the condition that at chi=0 the solution upsilon lies in the manifold generated by the Riemann invariants of the outgoing characteristics. For the equations of gas dynamics with an outflow boundary at chi=0 this condition may be written c/sub upsilon/..gamma..arho/sub t/+cupsilon..gamma..rho/sub t/+arhoS/sub t/=0, where a is the sound speed.},

doi = {10.1016/0021-9991(79)90100-1},

journal = {J. Comput. Phys.; (United States)},

number = ,

volume = 30:2,

place = {United States},

year = {1979},

month = {2}

}