Velocity-Correction Projection Methods For Incompressible Flows
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Vector and scalar penalty-projection methods - for incompressible and variable density flows
This work deals with the solution of Navier-Stokes equations governing incompressible flows with variable density, e.g. [10], or dilatable flows for which the Boussinesq approximation is no more valid like low Mach number flows, e.g. [5]. In these cases, the divergence constraint makes the fully-coupled system to solve at each time step for the velocity and dynamic pressure very ill-conditioned...
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We introduce and study a new class of projection methods—namely, the velocitycorrection methods in standard form and in rotational form—for solving the unsteady incompressible Navier–Stokes equations. We show that the rotational form provides improved error estimates in terms of the H1-norm for the velocity and of the L2-norm for the pressure. We also show that the class of fractional-step meth...
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