Coercive multidomain algorithms for incompressible fluid dynamics
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Data
1998
Autori
Trotta, Rosa Loredana
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Abstract
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.
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Keywords
Navier-Stokes equations , fluid dynamics equations