Stability and finite element approximation of phase change models for natural convection in porous media

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:360

Article

Woodfield, James^1,2,3  Alvarez, Mario⁴  Gomez-Vargas, Bryan^1,4,5,6  Ruiz-Baier, Ricardo¹ 

[1] Univ Oxford, Math Inst, A Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[2] Univ Reading, EPSRC CDT Math Planet Earth, Reading, Berks, England

[3] Imperial Coll London, London, England

[4] Univ Costa Rica, Sede Occidente, Secc Matemat, San Ramon De Alajuela, Costa Rica

[5] Univ Concepcion, CI2MA, Casilla 160-C, Concepcion, Chile

[6] Univ Concepcion, Dept Ingn Matemat, Casilla 160-C, Concepcion, Chile

关键词: Natural convection;    Viscous flow in porous media;    Finite element methods;    Change of phase;    Differentially heated cavity;   

DOI  :  10.1016/j.cam.2019.04.003

来源: Elsevier

【 摘 要 】

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. (C) 2019 The Authors. Published by Elsevier B.V.

【 授权许可】

Free