Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges since these systems enable ever-increasing size and complexity. In recent years, there has been renewed interest in developing multira...
Published in Lobachevskii Journal of Mathematics
AbstractGas cavities are deposits of gas, which monitoring is a very important problem for the geological surveys. The determination of the number of gas cavities from seismograms is an important problem, which solution is not possible without extra processing of the seismograms. In this work, we numerically solved the problem of exploring the infl...
Published in Lobachevskii Journal of Mathematics
AbstractThe exploration of the Arctic region is a very challenging and important problem today. One of the problems, connected with the Arctics’ investigation, is the ice strength change and measurement during the whole year. In this paper we present the results of the ice strength study using different numerical methods on the unstructured and str...
A flux reconstruction technique is presented to perform aeroacoustic computations using implicit high-order spatial schemes on multiblock structured grids with nonconforming interfaces. The use of such grids, with mesh spacing discontinuities across the block interfaces, eases local mesh refinements, simplifies the mesh generation process, and thus...
Published in Mathematical Models and Computer Simulations
To study the known problem on generating a regular grid by means of the Winslow method in a rectangular domain with a boundary kink known as a backstep, a high-accuracy numerical method for the inverse harmonic mapping of the unit square onto the domain with a certain mapping of the domain boundaries is developed. The behavior of mapping level line...
Published in Mathematical Models and Computer Simulations
A problem of constructing a structured countable grid in a two-dimensional domain by mapping a parametric domain with the given quadratic grid onto this two-dimensional domain is considered. The Dirichlet problem is solved for a system of quasi-linear elliptic differential second-order equations to find mapping functions. An additional local mappin...
Published in Computational Mathematics and Mathematical Physics
Generation of structured difference grids in two-dimensional nonconvex domains is considered using a mapping of a parametric domain with a given nondegenerate grid onto a physical domain. For that purpose, a harmonic mapping is first used, which is a diffeomorphism under certain conditions due to Rado’s theorem. Although the harmonic mapping is a d...
