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In a recent paper [4] we have proposed and analysed a suitable mathematical model which describes the coupling of the Navier-Stokes with the Oseen equations. In this paper we propose a numerical solution of the coupled problem by subdomain splitting. After a preliminary analysis, we prove a convergence result for an iterative algorithm that alternates the solution of the Navier-Stokes problem to the one of the Oseen problem.
In a recent paper [4] we have proposed and analysed
a suitable mathematical model
which describes the coupling of the Navier-Stokes with the
Oseen equations.
In this paper we propose a numerical solution of the coupled
problem by subdomain splitting.
After a preliminary analysis, we prove a convergence result for
an iterative algorithm that alternates the solution of the Navier-Stokes
problem to the one of the Oseen problem.
We consider the Navier-Stokes equations in unbounded domains of uniform -type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once....
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough
domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic
expansion techniques. The roughness elements are supposed to be periodic and the influence of the
rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady
Stokes problems and so they are calculated only...
We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force . We assume that is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if is a quasiperiodic function with respect to , then the attractor is a continuous image of a torus. Moreover the...
We study the global attractor of the non-autonomous 2D
Navier–Stokes system with time-dependent external force
g(x,t). We assume that g(x,t) is a translation
compact function and the corresponding Grashof number is small.
Then the global attractor has a simple structure: it is the
closure of all the values of the unique bounded complete
trajectory of the Navier–Stokes system. In particular, if
g(x,t) is a quasiperiodic function with respect to t,
then the attractor is a continuous image...
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