Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Semi-Implicit Formulations of the Navier--Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling

We present semi-implicit (IMEX) formulations of the compressible Navier-Stokes equations (NSE) for applications in nonhydrostatic atmospheric modeling. The compressible NSE in nonhydrostatic atmospheric modeling include buoyancy terms that require special handling if one wishes to extract the Schur complement form of the linear implicit problem. We present results for five different forms of th...

AIAA 99-3360 A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

A m ulti-grid, ux-diierence-split, nite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting ows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extension...

An Upwind-Differencing Scheme for the Incompressible Navier-Stokes Equations

A Convergent Numerical Scheme for the Compressible Navier-Stokes Equations

In this paper, the three-dimensional compressible Navier-Stokes equations are considered on a periodic domain. We propose a semi-discrete numerical scheme and derive a priori bounds that ensures that the resulting system of ordinary differential equations is solvable for any h > 0. An a posteriori examination that density remain uniformly bounded away from 0 will establish that a subsequence of...