An immersed boundary method for computing heat and fluid flow in porous media


Lopez Penha, David J. and Ghazaryan, Lilya and Geurts, Bernard J. and Stolz, Steffen and Nordlund, Markus (2010) An immersed boundary method for computing heat and fluid flow in porous media. In: Fifth European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, 14-17 June 2010, Lisbon, Portugal.

Abstract:A volume-penalizing immersed boundary (IB) method is presented that facilitates the computation of fluid flow in complex porous media. The computational domain is composed of a uniform Cartesian grid, and solid bodies are approximated on this grid using a series of grid cells (i.e., a ''staircase'' approximation). Solid bodies are distinguished from fluid regions using a binary phase-indicator function: Taking the value of ''1'' in the solid parts of the domain and ''0'' in the fluid parts. The effect of solid bodies on the flow is modeled using a source term in the momentum equations. The source term is active only within solid parts of the domain, and enforces the no-slip boundary condition. Fluid regions are governed by the incompressible Navier-Stokes equations. An extension of the IB method is proposed to tackle coupled fluid-solid heat transfer. The extended IB method is validated for Poiseuille flow, which allows for a direct comparison of the numerical results against a closed analytical solution. We subsequently apply the extended IB method to flow in a structured porous medium and focus on bulk properties such as the gradient of the average pressure and the Nusselt number. Reliable qualitative results were obtained with 16-32 grid points per singly-connected fluid region.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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