Premium
Segmented multigrid domain decomposition procedure for incompressible viscous flows
Author(s) -
Srinivasan Kumar,
Rubin Stanley G.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650151107
Subject(s) - multigrid method , laminar flow , domain decomposition methods , grid , computational fluid dynamics , boundary (topology) , polygon mesh , mesh generation , mathematics , navier–stokes equations , flow (mathematics) , geometry , computer science , compressibility , mathematical analysis , finite element method , mechanics , partial differential equation , physics , thermodynamics
The application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid‐dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier‐Stokes (NS) equations are approximated with a reduced Navier‐Stokes (RNS) system, that represents the lowest‐order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher‐order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co‐ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward‐facing step channel.