We report on recent progress towards the development of a 3D optimization capability for transonic ow at high Reynolds numbers. In this paper we demonstrate optimization based on the 3D laminar Navier-Stokes equation, and we present validation of the ow analysis scheme based on the 2D Navier-Stokes equations with turbulence modelling.

Upwind schemes for the Euler and Navier-Stokes equations may be broadly classified into two distinct classes: those based directly on the macroscopic Navier-Stokes equations and those based indirectly on the Navier-Stokes equations via the Boltzmann equation. The former, conventional approach represents the majority of current research. However, recently gas-kinetic methods have gained attentio...

The aim of this lecture is to give an overview on modern numerical methods for the computation of incompressible flows. We start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes ...

A general procedure to obtain analytic solutions of the linearized lattice Boltzmann equation for simple ows is developed. As examples, the solutions for the Poiseuille and the plane Couette ows in two-dimensional space are obtained and studied in detail. The solutions not only have a component which is the solution of the Navier-Stokes equation, they also include a kinetic component which cann...

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 direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as prop...

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier–Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers’s equa...

We construct the weakly nonlinear-dissipative approximate system for the general compressible Navier-Stokes system in a periodic domain. It was shown in [11] that because the Navier-Stokes system has an entropy structure, its approximate system will have Leray-like global weak solutions. These solutions decompose into an incompressible part governed by an incompressible Navier-Stokes system, an...

In this article, we propose to study two issues associated with the use of the incremental projection method for solving the incompressible Navier-Stokes equation. The first one is the combination of this time splitting algorithm with an adaptive local refinement method. The second one is the reduction of spurious velocities due to the right-hand side of the momentum balance. We propose a new v...

Abstract. We investigate a kinetic model for the sedimentation of dilute suspensions of rod-like particles under gravity, deduced by Helzel, Otto and Tzavaras (2011), which couples the impressible (Navier-)Stokes equation with the Fokker-Planck equation. With no-flux boundary condition for distribution function, we establish the existence and uniqueness of global weak solution to the two dimens...