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Global Riemann solver and front tracking approximation of three-component gas floods. (English) Zbl 1353.35202

The author’s study a \(2\times2\) system of non-strictly hyperbolic conservation laws arising in three-component gas flooding for enhanced oil recovery. The system is not strictly hyperbolic. In fact, along a curve in the domain one family is linearly degenerate, and along two other curves the system is parabolic degenerate. Through a constructive proof, authors show the existence and uniqueness for a solution of the global Riemann problem for a two-phase flow model with three-component gas flooding in reservoir simulation. The construction of the Riemann solution offers a front tracking algorithm, allowing numerical simulations for case studies.

MSC:

35L65 Hyperbolic conservation laws
35F55 Initial value problems for systems of nonlinear first-order PDEs
35Q35 PDEs in connection with fluid mechanics
35A35 Theoretical approximation in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
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