Abstract
We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging-diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.
| Original language | English |
|---|---|
| Pages (from-to) | 225-244 |
| Number of pages | 20 |
| Journal | Computers and Fluids |
| Volume | 118 |
| DOIs | |
| State | Published - Sep 2 2015 |
| Externally published | Yes |
Funding
The authors (M.D. and J.R.) would like to thank Bojan Popov and Jean-Luc Guermond for many fruitful discussions. This research was carried out under the auspices of the Idaho National Laboratory, a contractor of the U.S. Government under Contract No. DEAC07-05ID14517. Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.
| Funders | Funder number |
|---|---|
| U.S. Government | DEAC07-05ID14517 |
| Idaho National Laboratory |
Keywords
- Artificial viscosity
- Entropy viscosity method
- Euler equations with variable area
- Low-Mach regime
- Shock capturing