Stability and finite element approximation of phase change models for natural convection in porous media. (English) Zbl 1416.76133

Summary: In this paper we study a phase change problem for non-isothermal incompressible viscous flows. The underlying continuum is modelled as a viscous Newtonian fluid where the change of phase is either encoded in the viscosity itself, or in the Brinkman-Boussinesq approximation where the solidification process influences the drag directly. We address these and other modelling assumptions and their consequences in the simulation of differentially heated cavity flows of diverse type. A second order finite element method for the primal formulation of the problem in terms of velocity, temperature, and pressure is constructed, and we provide conditions for its stability. We finally present several numerical tests in 2D and 3D, corroborating the accuracy of the numerical scheme as well as illustrating key properties of the model.


76M10 Finite element methods applied to problems in fluid mechanics
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
80A22 Stefan problems, phase changes, etc.
Full Text: DOI


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