Coercive multidomain algorithms for incompressible fluid dynamics

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Trotta, Rosa Loredana
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The aim of this work is to present a new multidomain algorithm for the solution of Navier-Stokes equations. This is obtained by applying suitable domain decomposition methods, introduced for advection dominated advection-diffusion equations, in the context of fluid dynamics equations. The main novelty of out method [1] resides in the fact that we don't care about the local direction of the advective field on the interface Γ (as proposed in [2]), but we only need that the boundary value problems in each subdomain along the subdomain iterations are associated to a suitable coercive bilinear form. The extention of these methods to the resolution of the Navier-Stokes equations, has been obtained by facing the numerical solution focusing on the advection-diffusion phenomena, trying to circumvent the difficulties arising form the incompressibility constraint. This can be done using suitable fractional step methods, where the pressure does not play anymore the role of a Lagrange multiplier associated to the constraint. The method used is an incremental projection method, based on a reduced number of equations with respect to the classical projection algorithms, and, in particular, can be considered as a stabilization method. This choice allows the use of equal-order interpolation spaces, and therefore yields a considerable computational saving. The algorithms obtained are suited for parallel implementation.
Navier-Stokes equations , fluid dynamics equations