Numerical determination of the combustion rate of a gas suspension of coal dust in a propane-air mixture

The results of the numerical solution of the problem of the combustion rate of a coal-propane-air mixture are presented. The physical and mathematical formulation of the problem is based on the approaches of the dynamics of multiphase reacting media. The method for solving the problem is based on the algorithm for the decay of an arbitrary discontinuity. The dependences of the visible and normal combustion rate of the coal-propane-air mixture on the radius and the volumetric content of propane in the gas are obtained.

Vectorization of the Riemann solver using the AVX-512 instruction set

Numerical methods based on solving the Riemann problem of the decay of an arbitrary discontinuity are extremely demanding of computational resources. Applying the data of numerical methods to modern computational grids requires the use of a supercomputer. Among the various tools for improving the performance of supercomputer applications, we can emphasize the vectorization of program code. The AVX-512 instruction set has a number of unique features allowing to apply vectorization to the Riemann solver software context, which results in a significant acceleration of the solver.

Special discontinuities in models of continuum mechanics

Some models of continuum mechanics with possible special discontinuities are analyzed. It is of interest to study such discontinuities since they can generate the non-uniqueness of solutions in a problem of arbitrary discontinuity disintegration.