The stability of a flow in porous media relates to the velocity rate of injecting and withdrawing natural gases inside porous storage. We, thus, aim to analyze the stability of flows in porous media to accelerate the energy transition process. This research examines a flow model of a tangential–velocity discontinuity with porosity and viscosity changes in a three-dimensional (3D) compressible medium because of a co-existence of different gases in storage. The fluids are assumed to move in a relative motion where the plane y = 0 is a tangential-velocity discontinuity surface. We obtain that the critical value of the Mach number to stabilize a tangential discontinuity surface of flows via porous media is smaller than the one of flows in a plane. The critical value of the Mach number M to stabilize a discontinuity surface of the 3D flow is different by a factor compared to the two-dimensional (2D) flow. Here, θ is the angle between velocity and wavenumber vectors. Our results also show that the flow model with viscosity and porosity effects is stable faster than those without these terms. Our analysis is done for both infinite and finite flows. The effect of solid walls along the flow direction could suppress the instability, i.e., the tangential–discontinuity surface is stabilized faster.
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