Abstract:
A numerical scheme for the Brinkman–Forchheimer momentum equation modeling flow in a saturated porous duct is considered. There is no natural time variable we introduce a fictitious time variable, and, upon discretization of the two spatial variables, we obtain a system of ordinary differential equations in the fictitious time variable. The resulting system of ordinary differential equations is solved via a geometric numerical integration method known as the group preserving scheme. The group preserving scheme ensures the preservation of the group and cone structure of a system, resulting in a solution with the same asymptotic behavior as the original continuous system, avoiding spurious solutions or ghost fixed points. This fictitious time integration method allows us to obtain numerical solutions with low residual errors, and we compare our results favorably against analytical and numerical results present in the literature. Stability and convergence analysis of the method have been performed. Using these numerical solutions, we are able to discuss the effects of the various physical parameters, such as the inertial coefficient, viscosity of the fluid, effective viscosity, permeability of the porous media, and adverse applied pressure gradient on the fluid velocity through a porous duct modeled under the Brinkman–Forchheimer momentum equation.
Key words:Brinkman–Forchheimer momentum equation, flow in a saturated porous duct, fictitious time integration method, group preserving scheme.
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