Incompressible Navier-Stokes equation solvers based on lattice Boltzmann relaxation systems

Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations

A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations...

Alternative and Explicit Derivation of the Lattice Boltzmann Equation for the Unsteady Incompressible Navier-Stokes Equation

Incompressible Navier - Stokes and Euler Limits of the Boltzmann Equation

We consider solutions of the Boltzmann equation, in a d-dimensional torus, d = 2,3, for macroscopic times T = t / e N , e a: 1, t 2 0, when the space variations are on a macroscopic scale x = eN-’r , N 2 2, x in the unit torus. Let u ( x , r ) be, for t to, a smooth solution of the incompressible Navier Stokes equations (INS) for N = 2 and of the Incompressible Euler equation (IE) for N > 2. We...

On a Relaxation Approximation of the Incompressible Navier-stokes Equations

A comparison of preconditioners for incompressible Navier-Stokes solvers

We consider solution methods for large systems of linear equations that arise from the finite element discretization of the incompressible Navier–Stokes equations. These systems are of the so-called saddle point type, which means that there is a large block of zeros on the main diagonal. To solve these types of systems efficiently, several block preconditioners have been published. These types ...