CSAR Seminar
SPEAKER: Ratnesh Shukla, University of California at Los Angeles
TITLE:
Numerical Simulation of Viscous Incompressible Fluid Flow with Very
High-Order Compact Finite Difference Schemes on Non-Uniform Grids
DATE: Wednesday, January 31, 2007
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
Compact high-order finite difference schemes which consider as
unknowns, at each discretization point, not only the value of a
function, but also those of its first or higher derivatives have
recently attracted much attention due to their ability to resolve a
wide range of length scales. However, their application to practical
fluid flow problems has been restricted to relatively low orders of
accuracy due to the instability of high-order boundary closures on
uniform grids. In this talk, an approach to alleviating the instability
associated with the high-order boundary closures, through the use of
compact schemes on a non-uniform grid, with more grid points clustered
at the boundary of the computational domain will be discussed. A
convenient and efficient way of computing the coefficients of
arbitrarily high-order compact schemes, on a non-uniform grid, through
polynomial interpolation will be described. The accuracy and stability
of high-order non-uniform grid compact schemes for computation of the
linear wave equation and non-linear incompressible Navier-Stokes
equations will be demonstrated. Simulation results for the driven
cavity flow and uniform flow past an impulsively started cylinder, at
moderate to high Reynolds numbers, will be compared with benchmark
solutions. These comparisons will be used to comment on the resolution
properties of the high-order non-uniform grid compact schemes with
orders of accuracy ranging from four to twenty.
A brief description of the ongoing work on the development of an
inviscid vortex sheet model that enables the study of unsteady
separated flow past a two-dimensional deforming body will also be
presented.