Linear stability analysis of the explicit treatment of mobilities in non-Newtonian and non-Darcy porous media flow simulation

• Published in: Computational geosciences Vol. 18; no. 2; pp. 185 - 209
• Main Authors: Patacchini, Leonardo, de Loubens, Romain
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2014; Springer Nature B.V
• Subjects: Acceptability; Derivatives; Discretization; Earth and Environmental Science; Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Linear equations; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Media; Mobility; Original Paper; Porous materials; Porous media; Rendering; Simulation; Soil Science & Conservation; Stability analysis; Stabilization; Three dimensional; Semi-implicit; Stability analysis; Non-Newtonian; von Neumann; Non-Darcy
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-013-9395-6

A von Neumann stability analysis of the discretized conservation equation for single-phase porous media flows is performed, where non-Newtonian and non-Darcy effects are accounted for using a velocity (or mass flux)-dependent mobility factor. Comprehensive results in three dimensions for two low-order finite-volume discretizations typically encountered in reservoir simulation are provided, based on edge-centered and upstream cell-centered mobility calculations. It is found that common semi-implicit schemes, where the pressure gradient driving the flow is taken implicitly while the velocity-dependent mobility is evaluated explicitly, are subject to restrictions on the logarithmic derivative of mobility with respect to velocity. A remarkable new result is nevertheless obtained: for any physically acceptable strength of non-Newtonian and non-Darcy effects, there exists a stable and explicit method to evaluate the mobility, rendering the need to implement costly fully implicit schemes more difficult to justify.