Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements |
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Authors: | A Quarteroni G Sacchi Landriani A Valli |
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Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy;(2) Istituto di Analisi Numerical del C.N.R., Corso Carlo Alberto 5, I-27100 Pavia, Italy;(3) Dipartimento di Matematica, Università di Trento, I-38050 Povo (Trento), Italy |
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Abstract: | Summary A generalized Stokes problem is addressed in the framework of a domain decomposition method, in which the physical computational domain is partitioned into two subdomains
1 and
2.Three different situations are covered. In the former, the viscous terms are kept in both subdomains. Then we consider the case in which viscosity is dropped out everywhere in . Finally, a hybrid situation in which viscosity is dropped out only in
1 is addressed. The latter is motivated by physical applications.In all cases, correct transmission conditions across the interface between
1 and
2 are devised, and an iterative procedure involving the successive resolution of two subproblems is proposed.The numerical discretization is based upon appropriate finite elements, and stability and convergence analysis is carried out.We also prove that the iteration-by-subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size.This work was partially supported by CIRA S.p.A. under the contract Coupling of Euler and Navier-Stokes equations in hypersonic flows Deceased |
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Keywords: | 65N30 65N55 65N15 |
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