Solution of Problem for One Model of Relaxational Filtration by Probabilitly–Difference...

Solution of Problem for One Model of Relaxational Filtration by Probabilitly–Difference and Monte Carlo Methods Author: K.K. Shakenov Filtration in relaxationaly-compressed porous layers is described by the linear Darcy’s law. Relaxation kernels of the fi ltration and mass fl ow are of formulas (1) and (2). Perturbations front set instantly passes all considered domain making it by fi ltration domain. Equation for pressure as a function of space (x) and time (t) coordinates is of the form (2), with the beginning conditions (4) and (5). Velocity vector is defi ned as in (3) – it is Darcy’s law. Boundary conditions are defi ned after Dirichlet (6), Neumann (7) and as a mixed problem (8). The probability-difference and Monte-Carlo methods (random paths) are fully presented to solve the above boundary problems.

 

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