Accurate Projection Methods for the Incompressible Navier–Stokes Equations

Modified augmented Lagrangian preconditioners for the incompressible NavierStokes equations

We study different variants of the augmented Lagrangian (AL)-based block-triangular preconditioner introduced by the first two authors in [SIAM J. Sci. Comput. 2006; 28: 2095–2113]. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual method (GMRES) applied to various finite element and Marker-and-Cell discretizations of the Oseen problem in two and thr...

A class of fully second order accurate projection methods for solving the incompressible Navier–Stokes equations

In this paper, a continuous projection method is designed and analyzed. The continuous projection method consists of a set of partial differential equations which can be regarded as an approximation of the Navier–Stokes (N–S) equations in each time interval of a given time discretization. The local truncation error (LTE) analysis is applied to the continuous projection methods, which yields a s...

Accuracy of Projection Methods for the Incompressible Navier-Stokes Equations

Numerous papers have appeared in the literature over the past thirty years discussing projection-type methods for solving the incompressible Navier-Stokes equations. A recurring difficulty encountered is the proper choice of boundary conditions for the auxiliary variables in order to obtain at least second order accuracy in the computed solution. A further issue is the formula for the pressure ...

Velocity-Correction Projection Methods For Incompressible Flows

Lattice Boltzmann Model for the Incompressible NavierStokes Equation

In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...