Iterative substructuring methods for incompressible non‐isothermal flows and its application to indoor air flow simulation

Abstract

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,

Acceleration of a Domain Decomposition Method for Advection-Diffusion Problems

“…Moreover, regarding our application to flow problems (Knopp et al [2002]), in the turbulent case the solution usually has high-frequent components which may not be efficiently damped in our previous approach. As a remedy we propose a combination of the a posteriori control of the interface error with a cyclic multi-level version of the DDM:…”

“…It is used as a building block in a parallelized flow solver for the thermally driven incompressible Navier-Stokes problem, cf. Knopp et al [2002]. A fast convergence of the DDM is desirable, in particular for time-dependent problems.…”

Iterative Substructuring Methods for Indoor Air Flow Simulation

“…1 (left). For clarity of the presentation we assume ∂Ω = Γ 0 ≡ Γ W ; for the general case we refer to Knopp et al [2002] and Knopp [2003]. We start with the global problem with modified boundary conditions on Γ W compared to (2), (3):…”

“…where (·, ·) S denotes the inner product on some S and with an appropriate parameter set {δ T } T , see Knopp et al [2002]. Additionally, we use a (nonlinear) shock-capturing method, see Knopp et al [2002].…”

“…Additionally, we use a (nonlinear) shock-capturing method, see Knopp et al [2002]. For the Oseen problem (13), we define the discrete spaces…”