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Design of a well-balanced scheme for the numerical approximation of a three-phase flow model with discontinuous flux functions


In some recent researches, E. Abreu et al. built a numerical scheme for computing three phase flows in multidimensional porous media made of several rock types characterized by multiscale discontinuities. This scheme is based on a splitting strategy, the convection being computed separately of capillary diffusion. This is the first multidimensional method in the literature able to show strong numerical evidence of existence and structurally stable nonclassical waves for three-phase flow under excitations imposed by heterogeneity of porous media systems associated with the governing partial differential equations with discontinuous and spatially variable coefficients. On the other hand, C. Cancès et al. Developed a rigorous analysis of the singular effects linked to the brutal change of rock type on the solution of the simpler case of two-phase flows. C. Cancès particularly proved that this effect were of great importance on the behavior of the solution, even when the capillary pressure seemed to be neglected. We propose to take advantage at the intersection of our previous works to build a new conservative well-balanced scheme respecting the local equilibria linked to the capillary pressure discontinuities even in the pure convection step. We expect to sensibly improve the accuracy of the new well-balanced scheme without increasing too much the computational cost. Title: "Design of a well-balanced scheme for the numerical approximation of a three-phase flow model with discontinuous flux functions" (AU)

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(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
ABREU, EDUARDO. Numerical modelling of three-phase immiscible flow in heterogeneous porous media with gravitational effects. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 97, p. 234-259, MAR 2014. Web of Science Citations: 13.

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