Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases

On properties of aggregated regularized systems of equations for a homogeneous multicomponent gas mixture

“…This indicates the physical and, to a certain extent, mathematical correctness of these systems. Similar result has recently been given in papers 20,21 in the case of the QGD system for binary mixtures and in the absence of diffusion fluxes only.…”

“…The case of regularized Euler equations, when the physical coefficients of viscosity and heat conductivity equal 0, is also covered: then the use of artificial coefficients μ , λ and ϰ proportional to τ is assumed, see previous works 2–4 ; below their specific form is unimportant. In the case of a binary mixture ( ) with and , the discussed QGD equations have recently been derived in papers 20,21 by aggregating the QGD equations for inhomogeneous mixtures from Elizarova et al 18 In the same case, the above QHD equations can be derived quite similarly and even simpler from the QHD equations for inhomogeneous mixtures in Elizarova et al, 18, formulas (19)–(21) but we do not dwell on this in more detail here. The above QGD and QHD equations for multicomponent homogeneous mixtures are their natural generalizations.…”

“…[13][14][15][16][17] Various regularized QGD and QHD systems of equations for binary mixtures in the absence of chemical reactions, including both non-homogeneous mixtures (when not only the densities but also the velocities and temperatures of the components are different) and homogeneous ones (i.e., with the common velocity and temperature of the mixture components), have been constructed, discretized and successfully tested in numerical simulations including those in previous works. 3,[18][19][20][21][22][23] This paper studies the properties of aggregated QGD and QHD systems of equations for the homogeneous multicomponent gas mixture which are essential as a mathematical basis for the success of the mentioned discretizations. This is carried out in the unified manner for the both systems.…”

“…Important mathematical results on the properties of their solutions were proved, in particular, in papers 13–17 . Various regularized QGD and QHD systems of equations for binary mixtures in the absence of chemical reactions, including both non‐homogeneous mixtures (when not only the densities but also the velocities and temperatures of the components are different) and homogeneous ones (i.e., with the common velocity and temperature of the mixture components), have been constructed, discretized and successfully tested in numerical simulations including those in previous works 3,18–23 …”

The Eulerian–Lagrangian Approach for the Numerical Investigation of an Acoustic Field Generated by a High-Speed Gas-Droplet Flow

“…When this coefficient tends to zero, the QGD system of equations reduces to the conventional system for perfect gas mixture motion based on Navier-Stokes equations; e.g., (1)- (6). Detailed information about the regularized equations employed in this study can be found in the papers [29][30][31].…”