2015/02/02 by Prabir Daripa, Daripa, Prabir, Oscar Orellana +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Lattice Boltzmann Simulation Studies #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1502.00380
openalex publication_date 2015/02/02 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
We present a non-standard eigenvalue problem that arises in the linear\nstability of a three-layer Hele-Shaw model of enhanced oil recovery. A\nnonlinear transformation is introduced which allows reformulation of the\nnon-standard eigenvalue problem as a boundary value problem for Kummer's\nequation when the viscous profile of the middle layer is linear. Using the\nexisting body of works on Kummer's equation, we construct an exact solution of\nthe eigenvalue problem and provide the dispersion relation implicitly through\nthe existence criterion for the non-trivial solution. We also discuss the\nconvergence of the series solution. It is shown that this solution reduces to\nthe physically relevant solutions in two asymptotic limits: (i) when the linear\nviscous profile approaches a constant viscous profile; or (ii) when the length\nof the middle layer approaches zero.\n