# Riemann solutions for counterflow combustion in light porous foam

## Abstract

The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented.

- Authors:

- Universidade Federal de Juiz de Fora, Departamento de Matemática (Brazil)

- Publication Date:

- OSTI Identifier:
- 22769332

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; AIR; COMBUSTION; COMBUSTION WAVES; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS; SOLID FUELS; TRAVELLING WAVES

### Citation Formats

```
Chapiro, Grigori, and Senos, Laura.
```*Riemann solutions for counterflow combustion in light porous foam*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0420-6.

```
Chapiro, Grigori, & Senos, Laura.
```*Riemann solutions for counterflow combustion in light porous foam*. United States. doi:10.1007/S40314-017-0420-6.

```
Chapiro, Grigori, and Senos, Laura. Tue .
"Riemann solutions for counterflow combustion in light porous foam". United States. doi:10.1007/S40314-017-0420-6.
```

```
@article{osti_22769332,
```

title = {Riemann solutions for counterflow combustion in light porous foam},

author = {Chapiro, Grigori and Senos, Laura},

abstractNote = {The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented.},

doi = {10.1007/S40314-017-0420-6},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}