Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Minev P.   Angot P.   Guermond J.  

A Direction Splitting Algorithm for Flow Problems in Complex Geometries

Reporter: Minev P.

      The talk will present and analyze the stability and convergence properties of an extension of the direction splitting methods  towards problems in complex, possibly time dependent geometries. The idea for applying the direction splitting to complex geometries stems from the idea of the fictitious domain/penalty methods. Since the direction splitting allows for the use of direct solution methods small values of the penalty parameter do not affect adversely the performance of the algorithm. The new technique is still unconditionally stable for parabolic problems and retains the same convergence rate in both, time and space, as the Crank-Nicolson scheme. Numerical results indicate that this method can be applied also to the Navier-Stokes equations where the pressure Poisson equation is substituted with a composition of one dimensional operators in each direction. The method seems to be still unconditionally stable and second order accurate, although the analysis is not performed yet.
     This technique is highly parallelizable and the resulting parallel code scales excellently on a very large number of processors. Numerical results on a cluster of up to 1000 processors will be demonstrated.


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