Nowadays the mathematical modelling is widely spread for solving various scientific and engineering problems. One of the trends in the development of mathematical modelling is the creation of detailed mathematical models of physical and chemical processes (digital twins) in technical devices (engines, power plants, vehicles, etc.). The purpose of creating digital twins is opportunity to simulate the behavior of the original natural phenomenon or technical device under different conditions. For this purpose, it is necessary to offer more advanced methods of mathematical description of various physical and chemical processes, as well as the numerical methods of solving the model equations using the parallel supercomputers. The report presents new derivative-free description of physical and chemical processes (CFD, turbulence, chemical kinetics, elasticity theory, etc.) in the continuum approximation and the Robust Multigrid Technique for parallel solution of the model equations in discontinuous approximation. The results of this study will be of interest to software developers for modelling physical and chemical processes in power engineering, chemical technology and other branches of mechanical engineering and science.

Dr. Sergei Martynenko is a leading researcher of the Laboratory of physical modeling of two-phase flows of Joint Institute for High Temperatures of the Russian Academy of Sciences, a senior researcher of the Combustion and Explosion Department of the Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry of the Russian Academy of Sciences, professor of Bauman Moscow State Technical University and corresponding member of the Russian Engineering Academy. His research has focused on the mathematical modeling of physical and chemical processes, CFD and numerical heat transfer, parallel and high-performance computing, and multigrid methods. He has published over 100 papers and 6 books.