A Pressure-Based Composite Grid Method for the Navier-Stokes Equations

Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates

“…Because of this, the conservation laws automatically hold across block interfaces after convergence. This is in contrast to [26,27], where specific measures had to be taken to ensure conservation and to obtain a continuous pressure field across block interfaces. Domain decomposition is used inside the pressurecorrection method instead of 6ice 6ersa as in [26,27].…”

“…As opposed to [26,27,33], we solve the momentum and pressure equations separately over the composite domain, instead of solving these equations simultaneously in the subdomains. As opposed to [23-25,28 -30,33], we do not use a multi-grid method, but solve the subdomains accurately using the GMRES method, see [34,35].…”

“…Another important difference between our method and those of [26][27][28][29][30] is that we use a minimal overlap instead of an arbitrary overlap. With minimal overlap, it is meant here that the overlap area approaches zero as the mesh is refined.…”

“…In [26,27], the domain decomposition method consists of solving both velocity and pressure on each subdomain simultaneously. This causes a difficulty with pressure levels in the subdomains, which must be matched after the computation since they are only determined up to a constant.…”

Domain decomposition for the incompressible Navier-Stokes equations: solving subdomain problems accurately and inaccurately

“…The above discussion can easily be extended to the general multidomain case. Also, extensions to irregular intersections are possible (see [20,22,32] for examples).…”