We consider methods for the numerical simulations of variable density incompressible fluids, modelled by the Navier-Stokes equations. Variable density problems arise, for instance, in interfaces between fluids of different densities in multiphase flows such as appearing in porous media problems. We show that by solving the Navier-Stokes equation for the momentum variable instead of the velocity...

Q = (& is a symmetric negative semidefinite N x N matrix which has a $-dimensional nullspace X( 1 4 d < N) and Q%~ f 0; er = diag(v,), where the numbers (vJ are real and distinct; f is an N-tupIe of nice functions of x. The Navier-Stokes equations are the second in a hierarchy of approximate equations (the first being Euler) for the hydrodynamical moments of solutions of Eq. (1.1) with E = 1. F...

Implicit-explicit (IMEX) multistep methods are very useful for the time discretiza-tion of convection diffusion PDE problems such as the Burgers equations and also the incompressible Navier-Stokes equations. Semi-discretization in space of the latter typically gives rise to an index 2 differential-algebraic (DAE) system of equations. Runge-Kutta (RK) methods have been considered for the time di...

to perhaps the fact that the turbulence model equations are solved only to obtain the eddy viscosity and also the Many researchers use a time-lagged or loosely coupled approach in solving the Navier–Stokes equations and two-equation turbuconvenience of simply adding separate routines to an exlence model equations in a time-marching method. The Navier– isting Navier–Stokes code. Consequently, ma...

The unfitted finite element methods have emerged as a popular alternative to classical for the solution of partial differential equations and allow modeling arbitrary geometries without need boundary-conforming mesh. On other hand, efficient resultant system is challenging task because numerical ill-conditioning that typically entails from formulation such methods. We use an adaptive geometric ...