Staggered grids discretization in three-dimensional Darcy convection

Details Staggered grids discretization in three-dimensional Darcy convection Staggered grids discretization in three-dimensional Darcy convection

2007-10-28

arxiv.org/abs/0710.5284v2

Nonlinear Sciences

Chaotic Dynamics

20 pages, 9 figures

Scientific paper

10.1016/j.cpc.2008.02.004

We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated using special schemes. Two problems with different boundary conditions are considered to study scenarios of instability of the state of rest. Branching off of a continuous family of steady states was detected for the problem with zero heat fluxes on two opposite lateral planes.

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