Placement and orientation of a graft may adversely affect upstream flow, with the degree of effect dependent on geometric factors of downstream position and graft angle.
The convergence rates of explicit agglomeration multigrid algorithms for turbulent flow problems are significantly worse than for inviscid flow problems. Two techniques for reducing numerical stiffness are investigated and compared. Directional coarsening, controlled by the parameter β, alters the agglomeration algorithm to generate coarse grids that reduce localized cell stretching. Line-implicit smoothing, controlled by the parameter α, adds implicit terms to the preconditioner along one-dimensional lines constructed on the mesh. Optimal values of β and α are presented for structured and hybrid unstructured meshes. A factor of two improvement in asymptotic convergence rates has been demonstrated. Substantial improvements in CPU time can be obtained for a five-order residual reduction.
A two-dimensional agglomeration multigrid solver is presented for the computation of steady turbulent ows on unstructured grids. The solver utilizes a nite-volume method to solve the Favre-averaged compressible Navier-Stokes equations. Utilizing a variety of source grids, an agglomeration process is used to automatically generate coarse grids suitable for use with a multigrid solver. Variations of the agglomeration algorithm including directional coarsening are presented. Programming issues with respect to the solver are discussed. Results are presented demonstrating the accuracy and e ciency of the solver, and the e ect of directional coarsening on multigrid convergence rates.
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