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SUMMARYThe parallel solution of the incompressible Navier-Stokes equations coupled with the energy equation is considered. For turbulent ows, the k= model together with a modiÿed wall-function concept is used. The iterative process requires the fast solution of advection-di usion reaction and Oseen-type problems. These linearized problems are discretized using stabilized ÿnite element methods. We apply a coarsegranular iterative substructuring method which couples the subdomain problems via Robin-type interface conditions. Then we apply the approach to the simulation of indoor air ow problems. Copyright As the basic mathematical model we consider the (non-dimensional) incompressible, non-isothermal Reynolds averaged NavierStokes equations (RANS) with the eddy-viscosity hypothesis. Buoyancy e ects are taken into account using the Boussinesq approximation. We seek a velocity ÿeld u, a pressure p, and a temperature  as solutions of the coupled non-linear systemwith S(u):= 1 2 (∇u + ∇u T ), isobaric volume expansion coe cient ÿ, gravitational acceleration g, volumetric heat sourceq V and speciÿc heat capacity (at constant pressure) c p . Furthermore,

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SUMMARYThe non-isothermal, incompressible Navier-Stokes equations with Boussinesq approximation are considered as a model of turbulent indoor air flows. The transient calculation is based on the Reynolds-averaged Navier-Stokes problem using the k/ε-turbulence model or improved variants such as the v 2 − f model. The model is first discretized in time using backward-differencing schemes and then linearized using a Newton-type method per time step with emphasis on the proper calculation of (non-negative) turbulence quantities. The resulting auxiliary problems of Oseen type and of advection-diffusion-reaction type are solved using stabilized finite element method of residual type. Here we summarize some of our recent analytical results for higher-order methods and shock-capturing techniques. The numerical solution to the model in boundary layer regions is obtained using either adaptive wall functions if the k-ε model is used or a hybrid mesh with anisotropic refinement if the v 2 − f model is applied. Besides the standard flow quantities, it is possible to calculate quantities such as the age of the air. Such quantities are used to develop criteria for the evaluation of the efficiency of air exchange in a room. The quality of the numerical simulations is demonstrated for typical benchmark problems.