A control-volume finite-element method is used for simulations of flows through coupled fluid-saturated porous and open domains. The Brinkman-Forchheimer equations are used to model the flow in the porous domain. Modeling at the interface is emphasized, and full consistency is ensured. No special modifications need to be implemented in the numerical procedures and computer codes developed to deal primarily with flows in open domains, the interface conditions being treated in a consistent and natural way. Three illustrative examples involving flows parallel to the interface, flows normal to the interface, and combined parallel-normal flows are presented.
SUMMARYThe formulation of a control-volume-based finite element method (CVFEM) for axisymmetric, twodimensional, incompressible fluid flow and heat transfer in irregular-shaped domains is presented. The calculation domain is discretized into torus-shaped elements and control volumes. In a longitudinal cross-sectional plane. these elements are three-node triangles. and the control volumes are polygons obtained by joining the centroids of the three-node triangles to the mid-points of the sides. Two different interpolation schemes are proposed for the scalar-dependent variables in the advection terms: a floworiented upwind function, and a mass-weighted upwind function that guarantees that the discretized advection terms contribute positively to the coefficients in the discretized equations. In the discretization of diffusion transport terms, the dependent variables are interpolated linearly. An iterative sequential variable adjustment algorithm is used to solve the discretized equations for the velocity components, pressure and other scalar-dependent variables of interest. The capabilities of the proposed CVFEM are demonstrated by its application to four different example problems. The numerical solutions are compared with the results of independent numerical and experimental investigations. These comparisons are quite encouraging.
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