Volume 36, Issue 2

The work is devoted to the application of Runge–Kutta discontinuous Galerkin (RKDG) method for solving Baer–Nunziato hyperbolic model for nonequilibrium two-phase flows. The approach is based on the application of the simple WENO limiter directly to the conservative variables. Mathematical model and the corresponding numerical algorithm are described. The results of numerical simulations for 1D and 2D tests are presented and discussed.

The paper is focused on construction of computational models of stratus clouds using remote sensing data and on Monte Carlo analysis of optical radiation transfer peculiarities caused by stochastic structure of clouds.

The paper is focused on computation of stable periodic solutions to systems of delay differential equations modelling the dynamics of infectious diseases and immune response. The method proposed here is described by an example of the well-known model of dynamics of experimental infection caused by lymphocytic choriomeningitis viruses. It includes the relaxation method for forming an approximate periodic solution, a method for estimating the approximate period of this solution based on the Fourier series expansion, and a Newton-type method for refining the approximate period and periodic solution. The results of numerical experiments are presented and discussed. The proposed method is compared to known ones.

Turbulent mixing, ignition, and flame stabilization in the non-premixed supersonic hydrogen-air flow is numerically modelled in a near-wall region. Mixing algorithm based on the turbulence approach SARANS (Reynolds Averaged Navier–Stokes equations closed with Spalart–Allmaras turbulence model) with a diffusion model and a detailed kinetic model for hydrogen-air chemical reactions are employed. The system of governing equations that consists of basic conservation laws and the turbulence model equation is solved in a coupled manner with the LU–SGS–GMRES method. The model is applied to simulate the process of hydrogen injection into a M = 2.44 air flow with their subsequent mixing, ignition, and combustion in the Burrows– Kurkov chamber. The results are compared to available experimental and reference computational data. All calculations are carried out on the ‘MVS-10P’ JSCC RAS supercomputer cluster.

Ensemble numerical experiments for winter seasons of 1980–2014 were carried out with the use of the mathematical climate model of the Institute of Numerical Mathematics (INM) of the Russian Academy of Sciences developed initially for multi-year climate forecasts. Based on the results obtained in this research, a qualitative assessment of the reproduction of the North Atlantic (NAO) and Pacific-North American (PNA) oscillation indiceswas obtained. It was shown that the INM-CM5-0 climate model has a very high predictability of the winter NAO index and one, but not unique reason for this is the predictability of the stratospheric variability in the INM RAS model. The analysis of the quality of reproduction of the PNA index on a seasonal time scale for the INM-CM5-0 model has shown an acceptable result.