We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties of the equation, derive simple formulas for the squared speed of sound, and present an alternative proof for a formula that relates it to the squared Wood speed of sound; also, a short derivation of the pressure balance equation is given. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). Previously, regularizations of such types were developed only for the homogeneous mixtures of perfect polytropic gases, and it was unclear how to cover the case considered here. In the 1D case, based on these regularizations, we construct new explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and provide numerical results for various flows with shock waves.
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November 2023
Research Article|
November 21 2023
On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations
A. Zlotnik
;
A. Zlotnik
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Validation)
Department of Mathematics, Higher School of Economics University
, Pokrovskii Bd. 11, 109028 Moscow, Russia
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T. Lomonosov
T. Lomonosov
b)
(Software, Validation, Visualization, Writing – original draft)
Department of Mathematics, Higher School of Economics University
, Pokrovskii Bd. 11, 109028 Moscow, Russia
b)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
b)Author to whom correspondence should be addressed: [email protected]
a)
Also at Keldysh Institute of Applied Mathematics, Miusskaya Sqr., 4, 125047 Moscow, Russia. Electronic mail: [email protected]
Chaos 33, 113128 (2023)
Article history
Received:
May 22 2023
Accepted:
October 30 2023
Citation
A. Zlotnik, T. Lomonosov; On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations. Chaos 1 November 2023; 33 (11): 113128. https://doi.org/10.1063/5.0159201
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