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Efficient three-dimensional FEM based algorithm for the solution of convection in partly porous domains. (English) Zbl 1227.80007

Summary: The authors present an efficient three-dimensional algorithm, based on the fully explicit matrix inversion free finite element version of the Characteristic Based Split (CBS) scheme, and apply it for the first time to the simulation of complex thermo-fluid-dynamic problems in domains containing simultaneously a fluid and a porous layer. The stability analysis recently developed for the two-dimensional version of the algorithm is here extended to the three-dimensional version. Unstructured grids have been successfully employed to solve complex interface problems. The present code produces an effective solution for complex 3D problems, and does not require large computing resources. The advantages deriving from the algorithm’s stability, the use of unstructured meshes and the low computing requirements make the present three-dimensional procedure a powerful and flexible tool for efficient modeling of real life problems. The present 3D code is used to solve both forced and natural convection in partially porous domains.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
76R05 Forced convection
76R10 Free convection
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
35Q30 Navier-Stokes equations
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