By Donald A. Drew (auth.), Professor Wolfgang Wendland, Professor Messoud Efendiev (eds.)
The research and simulation of multifield difficulties have lately develop into essentially the most real and bright parts of analysis. even though the person subproblems of advanced technical and actual phenomena usually are understood individually, their interplay and coupling create not just new problems but in addition an entire new point and caliber of interacting coupled box difficulties. provided via top specialists this publication contains fresh leads to those fields from the overseas convention on Multifield difficulties, April 8-10, 2002 on the collage of Stuttgart, Germany.
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Additional resources for Analysis and Simulation of Multifield Problems
We see that the contractivity constant Q is crucial, and the convergence depends strongly on the ordering of the subsystems in the block-Gauss-Seidel solution strategy. If enough iterations are performed, essentially only the error components from the single system integrators remain. If we have c:~n) = O((L1t)P) and c~n) = O((Llt)q) as convergence orders for the single system integrators, we obtain c5(n) = O((L1t)min(p,q)), in contrast to the staggering scheme where we only have O(Llt). We now want to summerise for our example of FSI how the solution strategy, the grouping of the systems and algebraic constraint equations, and the order in the Gauss-Seidel process determine the contraction constant Q.
The two subsystems (9a,9b) may be solved independently of each other, but the method, considered for the system as a whole, is explicit, and will again introduce limitations connected with a critical time step associated to the global system. To circumvent this, generally we have to introduce a global coupling, although there are methods to retain at least the linear stability characteristics in the staggered approach [21,14,41]. We should mention that naturally the partly implicit variant of (4b) is also possible: After performing (9a), replace (9b) by (n) _ A.
In: Bathe K-J. ) Computational Fluid and Solid Mechanics. Elsevier, Amsterdam 30. Matthies H. , Steindorf J. (2002) Fully coupled fluid-structure interaction using weak coupling. Proc. in Appl. Math. and Mech. 1(1), 37-38 31. Matthies H. , Steindorf J. (2002) Partitioned Strong Coupling Algorithms for Fluid-Structure-Interaction. submitted to Computers & Structures 32. , Mackens W. (1995) Newton-coupling of fixed point iterations. , Wittum G. ) Numerical Treatment of Coupled Systems. Vieweg, Braunschweig Strong Coupling Methods 35 33.