Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics
Eric Blayo; Antoine Rousseau; Manel Tayachi
The SMAI journal of computational mathematics, Volume 3  (2017), p. 117-137

We propose in the present work an extension of the Schwarz waveform relaxation method to the case of viscous shallow water system with advection term. We first show the difficulties that arise when approximating the Dirichlet to Neumann operators if we consider an asymptotic analysis based on large Reynolds number regime and a small domain aspect ratio. Therefore we focus on the design of a Schwarz algorithm with Robin like boundary conditions. We prove the well-posedness and the convergence of the algorithm.

Published online : 2017-09-15
DOI : https://doi.org/10.5802/smai-jcm.22
Classification:  65M55
Keywords: Schwarz waveform relaxation, shallow water equations, domain decomposition, absorbing operators
@article{SMAI-JCM_2017__3__117_0,
     author = {Eric Blayo and Antoine Rousseau and Manel Tayachi},
     title = {Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics},
     journal = {The SMAI journal of computational mathematics},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {3},
     year = {2017},
     pages = {117-137},
     doi = {10.5802/smai-jcm.22},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2017__3__117_0}
}
Blayo, Eric; Rousseau, Antoine; Tayachi, Manel. Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics. The SMAI journal of computational mathematics, Volume 3 (2017) , pp. 117-137. doi : 10.5802/smai-jcm.22. https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2017__3__117_0/

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