Sinsoysal, BahaddinRasulov, MahirIskenderova, Revane2024-06-132024-06-13202497807354483600094-243X10.1063/5.01948052-s2.0-85186093825https://doi.org/10.1063/5.0194805https://hdl.handle.net/11501/9986th International Conference on Analysis and Applied Mathematics, ICAAM 2022 -- Antalya -- 31 October-6 November 2022In this paper, a new numerical method is proposed for solving the generalized Buckley-Leverett problem, which describes the movement of two-phase mixtures in Bazhenov bed sediments in a class of discontinuous functions. For this aim, an auxiliary problem that has some advantages over the main problem and is equivalent to the main problem in a definite sense is introduced. By developing an original finite difference method obtained via advantages of the auxiliary problem, it is proposed that the efficient and economical numerical algorithms from a computer point of view for finding the weak solution of the main problem. In addition to these, the auxiliary problem also allows us to obtain the weak solution in a class of discontinuous functions, which accurately describes all physical properties of the problem.eninfo:eu-repo/semantics/closedAccessConference Object1Q43085