Two-level iteration penalty methods for the incompressible flows

An Adaptive Level Set Approach For Incompressible Two-Phase Flows

In Sussman, Smereka and Osher (1994), a numerical method using the level set approach was formulated for solving incompressible two-phase ow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the e ect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level ...

A finite element penalty-projection method for incompressible flows

The penalty–projection method for the solution of Navier–Stokes equations may be viewed as a projection scheme where an augmentation term is added in the first stage, namely the solution of the momentum balance equation, to constrain the divergence of the predicted velocity field. After a presentation of the scheme in the time semi-discrete formulation, then in fully discrete form for a finite ...

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...

Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in [2, 3] to the (non-consistent) super penalty discontinuous Galerkin methods introduced in [5] and [8]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments confirming the sharpness of the theoretical results. AMS s...

Velocity-Correction Projection Methods For Incompressible Flows