AbstractComputer simulations may contribute significantly to the optimal design of air‐conditioning systems. To capture the effects of partially permeable walls such as bookshelves on the movement of air and heat, it is necessary to extend the density‐dependent Navier‐Stokes equations by an additional friction term. The finite element technique is convenient to approximate the extended equations in spatial co‐ordinates. For the time co‐ordinate a recently proposed semi‐implicit finite difference method is very efficient in terms of accuracy and computational complexity. A pressure correction approach is most appropriate to decouple the primitive variables in the extended Navier‐Stokes equations. The resulting algorithm has the interesting feature that small symmetric positive definite systems of equations can be solved sequentially for each of the primitive variables. Iterative solution of the systems of equations with preconditioned conjugate gradients combined with a compressed storage scheme allows fine grid computations at affordable costs. As an example a two‐dimensional version of the code was applied to an enclosure which was heated from the side and contained a porous wall. The time‐dependent computational results are compared with
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