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A new class of truly consistent splitting schemes for incompressible flows. (English) Zbl 1032.76529

Summary: A new class of splitting schemes for incompressible flows is introduced. The new schemes are based on a weak form of the pressure Poisson equation and, at each time step, only require to solve a set of Helmholtz-type equations for the velocity and a Poisson equation (in the weak form) for the pressure, just as pressure-correction and velocity-correction schemes. However, unlike pressure-correction and velocity-correction schemes, the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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