Applied Numerical Mathematics 55 (2005) 69–82 www.elsevier.com/locate/apnum Cosymmetry preserving finite-difference methods for convection equations in a porous medium B. Karasözen a,∗ , V.G. Tsybulin b a Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara 06531, Turkey b Department of Mathematics and Mechanics, Rostov State University, Rostov on Don, Russia Available online 10 December 2004 Abstract The finite-difference discretizations for the planar problem of natural convection of incompressible fluid in a porous medium which preserve the cosymmetry property and discrete symmetries are presented. The equations in stream function and temperature are computed using staggered and non-staggered schemes in uniform and non- uniform rectangular grids.  2004 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Darcy equation; Cosymmetry; Finite-difference methods; Staggered grids; Families of equilibria 1. Introduction New simulations impose additional requirements on the quality of numerical algorithms. The preser- vation of as many as possible physical properties after discretization of continuous problems modelled as partial or ordinary differential equations is extremely important. Construction of the numerical schemes, being mimetic to its continuous prototypes, is currently under development [9]. In the last decade many structure preserving methods such as symplectic and reversible integrators have been developed to ensure better properties of long-time solutions [7]. In computational hydrodynamics the Arakawa discretization [1] was the first that provided two quadratic conservation laws corresponding to the energy and the en- strophy for two-dimensional Euler equations as well as a linear conservation law for mean vorticity. The * Corresponding author. E-mail address: bulent@metu.edu.tr (B. Karasözen). 0168-9274/$30.00  2004 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.apnum.2004.10.008