Volume 31, Issue 4

A kinetically-based system of equations for three-phase porous media flow simulation is considered. A simple case with the following assumptions is discussed: phase transitions are absent, phases do not dissolve and do not mix, the rock compressibility is negligible. Such systems are under consideration in applied problems when the pressure changes slightly and thermal processes are absent, for example, in environmental problems. The continuity equation is modified via introduction of the regularizing term and the second-order time derivative. Due to conversion to the hyperbolic type the corresponding difference equation stability is improved. An explicit algorithm is developed and adapted to high-performance computing systems. High parallelization efficiency is achieved on a classical cluster as well as on a hybrid cluster with graphics accelerators.

The paper is focused on development of weighted Monte Carlo methods allowing one to estimate simultaneously the characteristics of the radiation field reflected from the medium based on a single Markov chain and in a sufficiently wide range of wavelengths. Such Markov chain is constructed with the use of a special ‘artificial’ scattering phase function whose choice is approximately optimized according to the criterion of minimum of the spectral maximum of the variance of estimates. The efficiency of the considered weighted method is studied on a model problem related to scattering of solar radiation by a cloud layer. The weighted method developed in the present article is aimed to supercomputer simulation.

A modification of the weighted statistical modelling of the evolution of an ensemble of interacting particles is constructed for approximate solution of a nonlinear kinetic equation. If the auxiliary weight exceeds one, we propose to use randomized branching of trajectory of the model ensemble of particles or its corresponding extension. Numerical analysis of constructed algorithms is performed for specifically formulated model problem on relaxation of a mixture of two gases with very different concentrations.

In the present paper we study features and abilities of the combined TVD+SPH method relative to problems of numerical simulation of long waves runup on a shore within the shallow water theory. The results obtained by this method are compared to analytic solutions and to the data of laboratory experiments. Examples of successful application of the TVD+SPH method are presented for the case of study of runup processes for weakly nonlinear and strongly nonlinear waves, and also for N -waves.

The present paper is focused on the mathematical model describing the dynamics of an artificial heart valve and the method of its numerical solution. The results of performance simulation are presented for the tricuspid valve of perfect form and the biological prosthesis ‘Uniline’.