PARALLEL ALGORITHM FOR IDENTIFICATION OF PARAMETERS OF THE MODEL OF SUSPENSION FILTRATION IN A POROUS MEDIUM
Keywords:
filtration, finite differences, inverse problem, mathematical model, parallel algorithm, porous medium, regularizationAbstract
The paper explores a mathematical model for suspension filtration in a porous medium, incorporating a mass balance equation for suspended particles and kinetic equa tions for both irreversible and reversible particle deposition. An inverse problem was formulated and solved numerically to determine four parameters of the model at once. Four parameters to find: the diffusion coefficient in the mass balance equation, deposition rate coefficients in the kinetic equations of both active and passive zones and reversible deposition re-entrainment coefficient. A first-order identification method was used for this purpose. The results show that when the initial approximations are close to the exact values of given parameters, the parameters are recovered with a small number of iterations. When the initial approximations deviate slightly from the given values, the number of iterations required to recover the parameters increases, but the coefficients are recovered with a sufficiently small error. It was found that when the initial approxi mations of the parameters are sufficiently far from the exact values of given parameters, the first-order identification method does not give good results, and the iterative process becomes divergent. In this case, a modified identification method using regularization was used to recover the parameters, and the parameters were recovered with sufficient accuracy. Taking into account that a large amount of calculations are performed during the inverse problem, a parallel algorithm was proposed for processing this problem. It was found that the program based on the parallelized algorithm works significantly faster than the original program.
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