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An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations. (English) Zbl 1059.76046
Summary: We develop a numerical method to solve unsteady incompressible Navier-Stokes equations. A fully implicit time advancement is employed to avoid Courant-Friedrichs-Lewy restriction, where Crank-Nicolson discretization is used both for diffusion and convection terms. Based on a block LU decomposition, velocity-pressure decoupling is achieved in conjunction with approximate factorization. The main emphasis is placed on the additional decoupling of intermediate velocity components with only \(n\)th time step velocity. The temporal second-order accuracy is preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving several test cases, in particular, the turbulent minimal channel flow unit.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Software:
FEATFLOW
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