Multi‐resolution simulation of double‐diffusive convection in porous media

J.W. Peterson (Texas Advanced Computing Center, The University of Texas at Austin, Austin, Texas, USA)
B.T. Murray (Department of Mechanical Engineering, SUNY Binghamton, Vestal, New York, USA)
G.F. Carey (Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 12 January 2010



The purpose of this paper is to consider double‐diffusive convection in a heated porous medium saturated with a fluid. Of particular interest is the case where the fluid has a stabilizing concentration gradient and small diffusivity.


A fully‐coupled stabilized finite element scheme and adaptive mesh refinement (AMR) methodology are introduced to solve the resulting coupled multiphysics application and resolve fine scale solution features. The code is written on top of the open source finite element library LibMesh, and is suitable for parallel, high‐performance simulations of large‐scale problems.


The stabilized adaptive finite element scheme is used to compute steady and unsteady onset of convection in a generalized Horton‐Rogers‐Lapwood problem in both two and three‐dimensional domains. A detailed study confirming the applicability of AMR in obtaining the predicted dependence of solutal Nusselt number on Lewis number is given. A semi‐permeable barrier version of the generalized HRL problem is also studied and is believed to present an interesting benchmark for AMR codes owing to the different boundary and internal layers present in the problem. Finally, some representative adaptive results in a complex 3D heated‐pipe geometry are presented.


This work demonstrates the feasibility of stabilized, adaptive finite element schemes for computing simple double‐diffusive flow models, and it represents an easily‐generalizable starting point for more complex calculations since it is based on a highly‐general finite element library. The complementary nature of h‐adaptivity and stabilized finite element techniques for this class of problem is demonstrated using particularly simple error indicators and stabilization parameters. Finally, an interesting double‐diffusive convection benchmark problem having a semi‐permeable barrier is suggested.



Peterson, J., Murray, B. and Carey, G. (2010), "Multi‐resolution simulation of double‐diffusive convection in porous media", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 1, pp. 37-65.

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