PUBLICATIONS

W. S. Don and D. Gottlieb,

Spectral Simulation of Unsteady Compressible Flow Past a Circular Cylinder,

in Spectral and High Order Methods for Partial Differential Equation (ed. C. Canuto and A. Quarteroni),

Elsevier Science Publishers, pp. 39-58, 1990.

S. Abarbanel, W. S. Don, D. Gottlieb, D. Rudy and J. Townsend,

Secondary frequencies in the wake of a circular cylinder with vortex shedding,

Journal of Fluid Mechanics, 225, pp. 557-574, 1991

W. S. Don,

Numerical Study of Pseudospectral Methods in Shock Wave Applications,

Journal of Computational Physics, 110, pp. 103-111, 1994

W. S. Don and D. Gottlieb,

The Chebyshev-Legendre Method : Implementing Legendre Method on Chebyshev Points,

SIAM Journal of Numerical Analysis, 31, No. 6, pp. 1519-1534, 1994

W. S. Don and A. Solomonoff,

Accuracy and Speed in Computing the Chebyshev Collocation Derivative,

SIAM Journal of Scientific Computing, 16, No. 6, pp. 1253-1268, 1995

W. S. Don and C. Quillen,

Numerical simulation of Reactive Flow, Part I : Resolution,

Journal of Computational Physics, 122, pp. 244-265, 1995

M. Carpenter, D. Gottlieb, S. Abarbanel and W. S. Don,

The Theoretical Accuracy of Runge-Kutta Time Discretizations for the Initial boundary Value

Problem : A Careful Study of the Boundary Error,

SIAM Journal of Scientific Computing, 16, No. 6, Nov. 1995

W. S. Don and A. Solomonoff,

Accuracy Enhancement for Higher Derivatives using Chebyshev Collocation and a Mapping Technique,

SIAM Journal of Scientific Computing, 18, No. 4, 1997

W. S. Don and D. Gottlieb,

High Order Methods for Complicated Flows Interacting with Shock Waves,

AIAA 97-0538

W. S. Don and D. Gottlieb,

Spectral Simulations of Supersonic Reactive Flows,

SIAM Journal of Numerical Analysis, 35, No. 6, pp. 2370-2384, 1998

B. Costa and W. S. Don,

On the computation of High Order Pseudospectral Derivatives,

Applied Numerical Mathematics, 33, No. 1, 151-159, 2000

W. S. Don, D. Gottlieb and J. H. Jung,

Multi-domain spectral method approach to supersonic combustion of recessed cavity flame-holders,

JANNAF 38th Combustion, 26th Airbreathing Propulsion, 20th Propulsion Systems Hazards,

and 2nd Modeling and Simulation Subcommittees Joint Meeting, Destin, FL, 8-12 April 2002

B. Sjogreen, H. C. Yee and W. S. Don,

Performance of Several High order Numerical Methods for Supersonic Combustion,

SIAM conference proceeding for the Ninth International Conference on Numerical Combustion,

Sorrento, Italy, 2002

W. S. Don, D. Gottlieb, L. Jameson and C. W. Shu,

High Order Numerical Methods for the Two Dimensional Richtmyer-Meshkov Instability, Part I.,

Conference proceeding for the International Workshop for the Physics of Compressible

Turbulence Mixing, Laser and Particle Beams, to be appeared.

W. S. Don, D. Gottlieb and J. H. Jung,

A multi-domain spectral method for supersonic reactive flows,

Journal of Computational Physics, 192, pp. 325-354, 2003

W. S. Don, D. Gottlieb, L. Jameson, O. Schilling and C. W. Shu,

Convergence of the Spectral methods for the incompressible Taylor-Green vortex simulation,

Journal of Scientific Computing, 24, No. 1, pp. 569-595, 2005

M. S. Min, M. S. Kaber and W. S. Don,

Fourier-Pade approximations and filtering for the spectral simulations of incompressible

Boussinesq convection problem,

Publications du Laboratorie Jacques-Louis Lions, R03021,

Mathematics of Computation, accepted.

B. Costa and W. S. Don,

Spectral Convergence of Mapped Chebyshev Methods,

Journal of Scientific Computing, submitted.

B. Costa and W. S. Don,

Hybrid Central-WENO Finite Difference Methods for Conservation Laws,

Journal of Computational and Applied Mathematics, accepted, 2006.

B. Costa and W. S. Don,

Multi-Domain Hybrid Spectral-WENO Methods for Hyperbolic Conservation Laws,

Journal of Computational Physics, submitted.

B. Costa, W. S. Don, D. Gottlieb and R. Sendersky,

Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws,

Communication in Computational Physics, 1, pp. 550-577, 2006

M. Latini, O. Schilling and W. S. Don,

Effects of order of WENO flux reconstruction and spatial resolution on reshocked

two-dimensional Richtmyer-Meshkov instability,

Journal of Computational Physics, submitted, 2006.

M. Latini, O. Schilling and W. S. Don,

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability.

Part 1. Comparison to experimental data and to amplitude growth model predictions,

Physics of Fluids, under revision, 2006.

M. Latini, O. Schilling and W. S. Don,

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability.

Part 2. Physics of reshock and mixing,

Physics of Fluids, under revision, 2006.