# coupled solver

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 August 9, 2008, 05:15 coupled solver #1 ztdep Guest   Posts: n/a Sponsored Links Dear friends: Could you plese give me some reference about how to solve the N-s equations in a coupled form. Generally, i use the segerated solver, that is solve u, solve v, then solve pressure equation. regards

 August 9, 2008, 10:05 Re: coupled solver #2 otd Guest   Posts: n/a Beam, Richard M. & R. W. Warming, "An Implicit Factored Scheme for the Compressible Navier-Stokes Equations", AIAA Journal, vol 16, no. 4, April, 1978, pp. 393-403. Briley, W. R. & H. McDonald, "Solution of the Multidimensional Compressible Navier-Stokes Equations by a Generalized Implicit Method", Journal of Computational Physics, vol. 24, pp. 372-397, 1977. These were widely regarded to be the same idea, same scheme, developed independently at NASA Ames in California (Beam & Warming) and Pratt & Whitney in Massachusetts (Briley & McDonald).

 August 12, 2008, 08:27 Re: coupled solver #3 Jed Guest   Posts: n/a The hard part is that the Jacobian is indefinite (a generalized saddle point problem) which is difficult to precondition. Normally you will want a Schur complement preconditioner, of which there are many varieties. These references are reasonably general, but should give you a good start. Good scalability is still obtainable, for instance (http://59A2.org/files/cheb-scaling.png) shows the results of some experiments I did this spring. The Stokes case uses GMRES preconditioned by a partial solve with an approximate Block LU decomposition where a V-cycle of AMG (ML in this case) is used in the approximate Schur complement. @article{benzi2005nss, title={{Numerical solution of saddle point problems}}, author={Benzi, M. and Golub, G.H. and Liesen, J.}, journal={Acta Numerica}, volume={14}, pages={1--137}, year={2005}, publisher={Cambridge Univ Press} } @article{deniet2007tps, title={{Two preconditioners for saddle point problems in fluid flows}}, author={de Niet, AC and Wubs, FW}, journal={Int. J. Numer. Meth. Fluids}, volume={54}, pages={355--377}, year={2007} }

 August 12, 2008, 10:03 Re: coupled solver #4 otd Guest   Posts: n/a True for a steady-state formulation. The original references (Beam and Warming, etc) are transient formulations that put 1/delt t on the diagonal so that the coefficient matrix is non-singular. This allows (in principal) solution of the linearized system by non-iterative methods. Ztdep now has two direct approaches with different tools and difficulties at his disposal.

 August 13, 2008, 06:30 Re: coupled solver #5 dontknow Guest   Posts: n/a Try The Integrated Space-Time Finite Volume Method by Philip J. Zwart, Waterloo, 1999 and M. Raw, Robustness of coupled algebraic multigrid for the NS-equations, AIAA Paper 96-0297, 1996 I think it is the solver CFX is using, I implemented it and it is very fast and robust...

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