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Mixed cells (multicomponent cells) emerging in the development of Lagrangian-Eulerian (ALE) or Eulerian numerical techniques for solving the gas dynamics and elastoplasticity equations in multicomponent media contain either interfaces between materials or a mixture of materials. There is a problem of correctly approximation of the equations in such cells and the ALE code accuracy and performance depend on how the problem is resolved. Many approximation methods use the equation splitting into two stages, one of which consists in solving a given equation in Lagrangian variables. If mixed cells are simulated, the system of equations describing the gas dynamics and elastoplasticity is unclosed and there is a need to introduce additional closure relations that will allow determining the thermodynamic parameters of components using the available data for the mixture of components, as a whole. The chapter presents a review of the equation closure methods and results of the methods verification using several test problems having exact solutions.

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Abstract:The paper presents the k- model equations of turbulence with a single set of constants chosen by the authors, which is appropriate to simulate a wide range of turbulent flows. The model validation has been performed for a number of flows and its main results are given in the paper. The turbulent mixing of flow with shear in the tangential velocity component is discussed in details. An analytical solution to the system of ordinary differential equations of the k- model of turbulent mixing has been found for the self-similar regime of flow. The model coefficients were chosen using simulation results for some simplest turbulent flows. The solution can be used for the verification of codes. The numerical simulation of the problem has been performed by the 2D code EGAK using this model. A good agreement of the numerical simulation results with the self-similar solution, 3D DNS results and known experimental data has been achieved. This allows stating that the k- model constants chosen by the authors are acceptable for the considered flow.