Numerical and analytical solution of the equation for the probability-density function

The article suggests a computational solution of the closed-form equation for the probability-density function (PDF) of the particles velocity distribution in the gas velocity random field. The particles motion occurs only due to the influence of the resistance force written in the Stokes approximation. We introduce an analytical solution for the PDF though the Green’s function of the Fokker-Plank-Kolmogorov equation. The numerical quadrature method is based on the conservative difference scheme of the first accuracy order in time and of the second order in velocity. The results of the numerical quadrature are collated with the analytical solution. We compare two difference schemes approximating the convectional summand: central differences and upwind differences.

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