Numerical research of non-isothermal filtration process in fractal medium with non-locality in time

Abstract

The difference scheme for the numerical solution of boundary problem for a system of equations for non-isothermal filtration with a Caputo derivative of fractional order on time is developed. Stability of the differential scheme is proved. Computational experiment in the analysis of solutions obtained has been done. Physical processes pass slowly in the fractal medium with non-locality in time. It is explained by the fact the occasionally wandering particle is being eliminated from the start place slowly, since not all directions of the movement become available for it. Values of pressure and temperature depending on the co-ordinate of layer radius and time calculated, and graphs of the dynamics pressure and temperature changes according to the layer radius and in depending on the time are built. Deceleration of the processes with time in the solutions for fractional derivatives which is characteristic for such medium has been established.