2025/06/10 by Luis Lozano, Furtado Frederico, Lozano, Luis Fernando +5
Computer Science · Engineering · Mathematics · #35L65 #76S05 #76T30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2506.09077
openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work presents the Riemann solution for three-phase flow in porous media under the condition that oil viscosity exceeds that of water and gas. We classify all Riemann solution problems for scenarios where the left states L lie along the edge G-W, and the right states R span nearly the entire saturation triangle, excluding small regions near the boundaries G-O and W-O. We use the wave curve method to determine the Riemann solution for initial and injection data within the above-mentioned class. This study extends previous analytical solutions, which were limited to right states near the corner O or within the quadrilateral O-E-U-D. Notably, this classification remains valid for all viscosity variations satisfying the inequalities \eqrefeq:classical, corresponding to viscosity regimes where the umbilic point is close to the vertex O. We verify the L1loc-stability of the Riemann solution with respect to variations in the data. While we do not establish the uniqueness of the Riemann solution, extensive numerical experiments confirm its validity. Our findings provide a comprehensive framework for understanding three-phase flow dynamics in porous media under a wide range of conditions.