On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation

Analytical and numerical peculiarities of solving nonlinear problems are considered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equation (KPI). KPI is represented in integro-differential form. Main attention is paid to the problem of asymptotical behavior of solution and appearance of nonphysical artefacts. The numerical solution is carried out by the finite difference method. For a correct representation of the boundary condition along the y axis in numerical simulation a method is proposed for introducing small artificial convection into the original equation in the indicated direction. Along with the introduction of artificial convection, the procedure of trimming of the integral on the bands adjacent to the upper and lower boundaries of the calculated region is used. The results obtained by numerical testing, showed sufficient accuracy and validity of this procedure.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ВЗАИМОДЕЙСТВИЯ НЕДОРАСШИРЕННОЙ СВЕРХЗВУКОВОЙ СТРУИ ГАЗА С ПЛОСКОЙ ПРЕГРАДОЙ

The results of numerical modeling based on the nonstationary Reynolds-averaged Navier – Stokes equations for the interaction of an underexpanded supersonic gas jet with a flat obstacle, which was established at different distances from the nozzle exit section are presented. The results of the calculations are presented in the form of the distribution of the Mach number and the density gradient in the calculated region, and the pressure and friction coefficients over the surface of the plate. The results of the numerical calculation are compared with the experimental data.

Calculation of metastable immiscibility region in the Al2O3–SiO2 system using molecular dynamics simulation

The metastable immiscibility region in the Al2O3–SiO2 system was calculated by conventional thermodynamic equations using thermodynamic parameters obtained from molecular dynamics simulation. The calculated miscibility gap has a consolute temperature of around 1500 °C at the critical composition of about 20 mol% Al2O3 and spreads more widely towards the Al2O3-rich composition side than the SiO2-rich side. The calculated miscibility gap in this study showed a fair agreement with that reported by Ban et al. [T. Ban, S. Hayashi, A. Yasumori, and K. Okada, J. Mater. Res. 11, 1421 (1996)] calculated by a regular solution model, but the present calculated region is somewhat narrower in the Al2O3-rich composition side than that reported by Ban et al.