Generalized fundamental solutions for unsteady viscous flows

Generalized fundamental solutions for unsteady viscous flows.

A number of closed-form fundamental solutions for generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two parts corresponding to a longitudinal wave and a transversal wave. As examples of application, the hydrodynamic forces acting on a sphere and on a circular cylinder...

Unsteady Viscous Flows and Stokes’s First Problem

Unsteady viscous flows and Stokes’s first problem are examined. Three problems are considered: unsteady Couette flow, unsteady Poiseuille flow, and unsteady boundary layer flow. The relationship between these three fundamental unsteady flows and Stokes’ first problem is illustrated. Scaling principles are used to deduce the short time and long time characteristics of these three problems. Asymp...

Essentially Compact Schemes for Unsteady Viscous Incompressible Flows

A new 4th order accurate finite difference scheme for the computation of unsteady viscous incompressible flows is introduced. The scheme is based on the vorticitystream function formulation. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. It is also very efficient, at every time step or Runge-Kutta stage, only two Pois...

Numerical Simulation of Unsteady Incompressible Viscous -Flows in Generalized Coordinate Systems

Viscous Computation of Steady/Unsteady Transonic Diffuser Flows

The lag model proposed by Olsen and Coakley (2001) is applied to simulate the steady and unsteady transonic flows in a diffuser. The unsteady flows are induced by imposing fluctuating back-pressures. A fully implicit time–accurate multigrid algorithm is used for solving the Navier-Stokes equations and the coupled k-ω turbulence model equations. Two test cases are investigated, one with a weak s...