Sharp Material Interface Limit of the Darcy–Boussinesq System

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Abstract
We investigate the sharp material interface limit of the Darcy–Boussinesq model for convection in layered porous media with diffused material interfaces, which allow a gradual transition of material parameters between different layers. We demonstrate that as the thickness of these transition layers approaches zero, the conventional sharp interface model with interfacial boundary conditions, commonly adopted by the fluids community, is recovered under the assumption of constant porosity. Our results validate the widely used sharp interface model by bridging it with the more physically realistic case of diffused material interfaces. This limiting process is singular and involves a boundary layer in the velocity field. Our analysis requires delicate estimates for elliptic and parabolic equations with discontinuous coefficients and the subtle validation of the boundary layer.
Funding Information
  • National Natural Science Foundation of China (12271237)
  • National Science Foundation (DMS2350129)

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