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SIAMAM
2011

On Solutions to Equilibrium Problems for Systems of Stiffened Gases

8 years 5 months ago
On Solutions to Equilibrium Problems for Systems of Stiffened Gases
We consider an isolated system of N immiscible fluids, each following a stiffened-gas equation of state. We consider the problem of calculating equilibrium states from the conserved fluid-mechanical properties, i.e., the partial densities and internal energies. We consider two cases; in each case mechanical equilibrium is assumed, but the fluids may or may not be in thermal equilibrium. For both cases, we address the issues of existence, uniqueness, and physical validity of equilibrium solutions. We derive necessary and sufficient conditions for physically valid solutions to exist, and prove that such solutions are unique. We show that for both cases, physically valid solutions can be expressed as the root of a monotonic function in one variable. We then formulate efficient algorithms which unconditionally guarantee global and quadratic convergence toward the physically valid solution. Key words. stiffened gas, existence, uniqueness AMS subject classifications. 76T30, 26C15 DOI. ...
Tore Flåtten, Alexandre Morin, Svend Tollak
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where SIAMAM
Authors Tore Flåtten, Alexandre Morin, Svend Tollak Munkejord
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