Incompressible Flow

4 Dynamically Incompressible Flow

General Methodologies for Incompressible Flow Design Problems

Two design methodologies based on Incomplete-Gradient adjoint approaches for ow problems governed by the incompressible Navier-Stokes (NS) equations are presented. The main features of the algorithms is that they avoid solving the adjoint equations, saving an important amount of CPU time. Furthermore, the methodologies are general in the sense that they do not depend on the geometry representat...

Convergence of gauge method for incompressible flow

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field a and a gauge variable φ, u = a +∇φ, was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and verifies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretizat...

Preconditioning Strategies for Models of Incompressible Flow

We describe some new preconditioning strategies for handling the algebraic systems of equations that arise from discretization of the incompressible Navier-Stokes equations. We demonstrate how these methods adapt in a straightforward manner to decisions on implicit or explicit time discretization, explore their use on a collection of benchmark problems, and show how they relate to classical tec...

Motion In A Gaussian , Incompressible Flow

We prove that the solution of a system of random ordinary di erential equations dX(t) dt = V(t;X(t)) with di usive scaling, X"(t) = "X( t " ), converges weakly to a Brownian Motion when " # 0. We assume that V(t;x), t 2 R, x 2 R is a d-dimensional, random, incompressible, stationary Gaussian eld which has mean zero and decorrelates in nite time.