A pressure based implicit procedure to solve the Euler and Navier-Stokes equation is developed to predict transonic viscous and inviscid flows around the pitching and heaving airfoils with a high reslution scheme. In this process, nonorthogonal and non moving mesh with collocated finite volume formulation are used. In order to simulate pitching or heaving airfoil, oscillation of flow boundary c...

The initial boundary value problems associated with the inviscid barotropic potential vorticity equation in the b-plane and its viscous analogue are considered. It is shown that the solution velocity to the viscous equation converges to the inviscid solution in a C1 sense for finite times and that, under additional smoothness assumptions on the inviscid flow, this convergence can be extended to...

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four travel...

The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system of two semi-infinite immiscible fluids of different densities are investigated analytically. The two fluids are assumed to be incompressible and homogenous. There are three systems to be considered: one with two inviscid fluids, one with an upper viscous and a lower inviscid fluid, and one with ...

This document provides a proof that the solutions to Convectively Filtered Burgers equation, will converge to the entropy solution of Inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of Inviscid Burgers equation. That solution is then shown to be the entropy solution.

We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

We explore the relation between viscous and inviscid stability of multi-dimensional shock fronts, by studying the Evans function associated with the viscous shock proole. Our main result, generalizing earlier one-dimensional calculations, is that the Evans function reduces in the long-wave limit to the Kreiss{Sakamoto{ Lopatinski determinant obtained by Majda in the inviscid case, multiplied by...

We establish global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction, which arises in Ocean dynamics. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. Although we follow some of their...