Yury Yanilkin

By Yury Yanilkin

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.

Part of the book: Lagrangian Mechanics

By Sofronov Vasily, Zhmailo Vadim and Yanilkin Yury

The paper presents an overview of benchmarks for non-ideal magnetohydrodynamics. These benchmarks include dissipative processes in the form of heat conduction, magnetic diffusion, and the Hall effect.

Part of the book: Numerical Simulations in Engineering and Science

By Yury Yanilkin, Vladimir Shmelev and Vadim Kolobyanin

The problem of correct calculation of the motion of a multicomponent (multimaterial) medium is the most serious problem for Lagrangian–Eulerian and Eulerian techniques, especially in multicomponent cells in the vicinity of interfaces. There are two main approaches to solving the advection equation for a multicomponent medium. The first approach is based on the identification of interfaces and determining their position at each time step by the concentration field. In this case, the interface can be explicitly distinguished or reconstructed by the concentration field. The latter algorithm is the basis of widely used methods such as VOF. The second approach involves the use of the particle or marker method. In this case, the material fluxes of substances are determined by the particles with which certain masses of substances bind. Both approaches have their own advantages and drawbacks. The advantages of the particle method consist in the Lagrangian representation of particles and the possibility of” drawbacks. The main disadvantage of the particle method is the strong non-monotonicity of the solution caused by the discrete transfer of mass and mass-related quantities from cell to cell. This paper describes a particle method that is free of this drawback. Monotonization of the particle method is performed by spliting the particles so that the volume of matter flowing out of the cell corresponds to the volume calculated according to standard schemes of Lagrangian–Eulerian and Eulerian methods. In order not to generate an infinite chain of spliting, further split particles are re-united when certain conditions are met. The method is developed for modeling 2D and 3D gas-dynamic flows with accompanying processes, in which it is necessary to preserve the history of the process at Lagrangian points.

Part of the book: Recent Advances in Numerical Simulations