NUMERICAL ALGORITHMS


On discretization error and its control in variational data assimilation, with D. Furbish, F.-X Le Dimet, P. Ngnepieba and Y. Wu, Tellus A (to appear), 2008.

Quantifying Parametric Uncertainty in the Rothermel Model, with E. Jimenez and S. Goodrick, International Journal of Wildland Fire, 2008, 17(3): **-** .

Three-dimensional curvelets for coherent vortex analysis of turbulence, with J. Ma, Applied Physics Letters 2007, 91: 184101.

Uncertainty Quantification of Rothermel Model Using a Sensitivity Derivative Enhanced Sampling Method, with E. Jimenez and S. Goodrick, Proceedings of the 2nd Fire Behavior and Fuels Conference: The Fire Environment -- Innovations, Management, and Policy, 2007, Destin, Florida, March 26-30, 2007.

Numerical Optimization of Radiated Engine Noise with Uncertain Wavenumbers, with Y. Cao and H. Yang, International Journal of Numerical Analysis and Modeling, 2007, 4 (3-4): 392-401.

A sharp interface method for incompressible two-phase flows, with M. Sussman, K. Smith, M. Ohta and R. Zhi-Wei, J. Computational Physics, 2007, 221 (2): 469-505.

Tracking discontinuities in hyperbolic conservation laws with spectral accuracy, with H. Touil and M. Sussman, J. Computational Physics, 2007, 225: 1810-1826.

An efficient sampling method for stochastic inverse problems, with P. Ngnepieba, Comput. Optim. Appl., 2007, 37 :121-138.

Unsteady Boundary Control for Optimal Control of Trailing Edge Noise , with G. Chen, AIAA 2006-2511, 12th AIAA/CEAS Aeroacoustics Conference, May 8-10, 2006, Cambridge, MA.

On the Expected Optimal Value and the Optimal Expected Value, with A.-M. Croicu, Applied Mathematics and Computation 2006, 180: 330-341.

On improving the predictive capability of turbulence models using evidence theory, with S.V. Poroseva, and S.L. Woodruff, AIAA J. 2006, 44: 1220-1228 .

A variance reduction method based on sensitivity derivatives, with Y. Cao, T. A. Zang and A. Zatezalo, Applied Numerical Mathematics 2006, 56: 800-813.

Placement of wind turbines using genetic algorithms, with A. A. Grady and M. M. Abdullah, Renewable Energy, 2005, 30: 259-270.

Stochastic approaches to uncertainty quantification in CFD simulations, with L. Mathelin and T.A. Zang, Numerical Algorithms, 2005, 38: 209-236.

Tip vortex noise prediction by SAURON: Superior Aeroacoustics Using Robust Overset Numerics, with A. Uzun and C. L. Streett, AIAA Paper 2005-2865, 11th AIAA /CEAS Aeroacoustics Conference, May 2005, Monterey, CA.

On improving the predictive capability of turbulence models using evidence theory, with S.V. Poroseva, and S.L. Woodruff, in Proceeding of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2005-1096, January, 2005, Reno, NV .

A comparative study of single-block versus multi-block jet flow computations, with A.Uzun and C. L. Streett, AIAA Journal, 2005, 43(5): 1143-1146.

A second order adaptive sharp interface method for incompressible multiphase flow, with M. Sussman, K. Smith, R. Zhi-Wei and V. Mihalef, Proceedings of the 3rd international conference on Computational Fluid Dynamics, Toronto, Canada, July 2004. 6 pages.

An efficient sampling method for stochastic optimal control problem, In Proceeding of 10th International Conference on Information Analysis and Synthesis ISAS 2004 and the International Conference on Cybernetics and Information Technologies, Systems and Applications: CITSA 2004. CITSA, Orlando, Florida, pp. 375-380, July 2004.

Application of the discontinuous spectral Galerkin method to groundwater flow, with S. Fagherazzi, P. Rasetarinera and D.J. Furbish, Advances in Water Resources, 2004, 27: 129-140.

A perfectly matched layer approach to the linearized shallow water equations models, with I.M. Navon, Monthly Weather Review, June 2004, 132: 1369-1378.

Numerical solution of the dam-break problem with a discontinuous galerkin method, with S. Fagherazzi, P. Rasetarinera, D. J. Furbish, Journal of Hydraulic Engineering, 2004, 130(6): 532-539.

On the exploitation of sensitivity derivatives for improving sampling methods, with Y. Cao and T. A. Zang, AIAA J., 2004, 42(4): 815-822.

Application of the discontinuous spectral Galerkin method to groundwater flow, with D. Furbish, P. Rasetarinera, Advances in Water Resources, 2004, 27(2): 129-140.

A Discontinuous Spectral Element Method for the Level Set equation , with M. Sussman, J. Scientific Computing, 19, pp. 479-500, 2003.

A Stochastic Collocation algorithm for uncertainty analysis, with L. Mathelin, NASA/CR-2003-212153, 2003.

Unsplit variables perfectly matched layers for the shallow water equations with Coriolis forces, with A. Abarbanel and D. Stanescu, Computational Geosciences, 2003, 7: 275-294.

An efficient Monte Carlo method for optimal control problems with uncertainty, with Y. Cao and T. A. Zang, Computational Optimization and Application, 2003, 26(3): 219-230.

An efficient implicit discontinuous spectral Galerkin method, with P. Rasetarinera, J. Comp. Physics, 2001, 172: 718-738.

Discontinuous spectral element solution of acoustic radiation from thin airfoils, with D. Kopriva and P. Rasetarinera, AIAA Journal, 2001, 39(11): 2070-75.

Direct-numerical and large-eddy simulations of a non-equilibrium turbulent Kolmogorov flow, with S. L. Woodruff and J. V. Shebalin,2001 preprint.

Dispersion analysis for discontinuous spectral element methods, with D. Stanescu and D. Kopriva, J. Sci. Computing, 2000, 15(2): 149-71.

Grid-size dependence in the large-eddy simulation of Kolmogorov flow, with S. L. Woodruff, and J. M. Seiner, AIAA Journal, 2000, 38(4): 600-604.

Discontinuous spectral element approximation of Maxwell's equations, with D. A. Kopriva and S. L. Woodruff, in Discontinuous Galerkin Methods, B. Cockburn, G. E. Karniadakis, and C.-W. Shu (Eds.), Lecture Notes in Computational Science and Engineering, Vol. 11, Springer, 1999.

Some remarks on the accuracy of a discontinuous Galerkin method, with P. Rasetarinera and F. Q. Hu, in Discontinuous Galerkin Methods, B. Cockburn, G. E. Karniadakis, and C.-W. Shu (Eds.), Lecture Notes in Computational Science and Engineering, Vol. 11, Springer, 1999.

Towards perfectly absorbing boundary conditions for Euler equations, with M. E. Hayder, and F. Q. Hu, AIAA Journal, 1999, 37(8): 912-18.

Analysis of the discontinuous Galerkin method for wave propagation problems, with F. Q. Hu, and P. Rasetarinera, J. Comp. Physics, 1999, 151: 921-946.

Nonlinear strong shock interactions: A shock-fitted approach, with G. Erlebacher, and T.L. Jackson, Theoretical Computational Fluid Dynamics, 1998, 11: 1-29.

Low-dissipation and dispersion Runge-Kutta schemes for computational acoustics, with F. Q. Hu and J. Manthey, J. Comp. Physics, 1996, 124: 177-191.

Linear and non-linear PSE for compressible boundary-layers, with C.-L. Chang, M. R. Malik and G. Erlebacher, ICASE Report No. 93-70, 1993.

Toward the large-eddy simulation of compressible turbulent flows, with Gordon Erlebacher, C. G. Speziale and T. A. Zang, J. Fluid Mech., 1992, 238: 155-185.

Toward the large-eddy simulation of compressible turbulent flows, with G. Erlebacher, C. Speziale and T. A. Zang, J. Fluid Mech., 1992, 238: 155-185.

Nonlinear evolution of a second-mode wave in supersonic boundary layers, with G. Erlebacher, Appl. Numer. Mathematics, 1991, 7(1): 73-91.

Direct simulation of compressible turbulence in a shear flow, with S. Sarkar and G. Erlebacher, Theor. Comput. Fluid Dynamics, 1991, 2(5/6): 291-305.

On the large-eddy simulation of transitional wall-bounded flows, with U. Piomelli, T. A. Zang and C. G. Speziale, Physics of Fluids A, 1990, 2: 257-265.

Parallelization of a three-dimensional compressible transition code, with G. Erlebacher and S. Bokhari, AIAA Journal, 1990, 28(8): 83-90.

Spectral methods for CFD, with T. A. Zang and C. L. Streett, ICASE Report No. 89-13, Von Karman Institute Lecture Notes, 1989.

Discussion of the potential and limitations of direct and large-eddy simulations, with C. G. Speziale and T. A. Zang, Lecture Notes in Physics, Springer-Verlag, 1989.

Mixing augmentation technique for hypervelocity scramjets, with A. Kumar and D. Bushnell, J. Propulsion and Power, 1989, 5(5): 514-522.

Spectral collocation methods, with D. A. Kopriva and A. T. Patera, Applied Numerical Mathematics, 1989, 5:177-208.

Computational fluid dynamics - a personal view, Lecture Notes in Physics, 323, D. L. Dwoyer, M. Y. Hussaini and R. G. Voigt, eds., Springer-Verlag, 1989, pp. 3-17.

A spectral collocation solution of the compressible stability Eigenvalue problem, NASA TP-2858, December 1988.

Spectral multigrid methods for the numerical simulations of turbulence, with G. Erlebacher and T. A. Zang, in Multigrid Methods, S. McCormick and K. Stuben, eds., Marcel-Dekker, 1988.

The subgrid-scale modeling of compressible turbulence, with C. G. Speziale, G. Erlebacher and T. A. Zang, Physics of Fluids, 1988, 31(4): 940-942.

A numerical model for supersonic reacting mixing layers, with J. P. Drummond and R. C. Rogers, Computer Meth. in Appl. Mech. and Engg., 1987, 64: 39-60.

Spectral methods in fluid dynamics, with T. A. Zang, Ann. Rev. Fluid Mech., 1987, 19: 339-367.

Multigrid methods for structural mechanics, with I. S. Raju, C. A. Bigelow and S. Ta'asan, NASA TM-87761, 1986.

Preconditioning methods for spectral multigrid calculations, with T. N. Phillips and T. A. Zang, IMA J. Num. Analysis, 1986, 6: 273-292.

Preconditioned conjugate residual methods for the solution of spectral equations, with Y. S. Wong and T. A. Zang, Computers and Fluids, 1986, 14(2): 85-95.

Efficient iterative techniques for the solution of spectral equations, with Y. S. Wong and T. A. Zang, Computers and Fluids, 1986, 14(2): 85-95.

Spectral methods for modeling supersonic chemically reacting flow fields, with J. P. Drummond and T. A. Zang, AIAA Journal, 1986, 24(9): 1461- 67.

On spectral multigrid methods for the time dependent Navier-Stokes equations, with T. A. Zang, J. of Applied Mathematics and Computation, 1986, 19: 359-372.

Second-order accurate explicit finite-difference schemes for waterhammer analysis, with M. H. Chaudhry, J. Fluids Engineering, 1985, 107: 523-528.

A spectral collocation method for the Navier Stokes equations, with M. R. Malik and T. A. Zang, J. Comp. Physics, 1985, 61: 64-88.

A three-dimensional spectral algorithm for simulation of transition and turbulence, with T. A. Zang, NASA CR-172561, 1985.

Fourier-Legendre spectral methods for incompressible channel flow, with T. A. Zang, Ninth International Conference on Numerical Methods in Fluid Dynamics, Saclay, France, June 25-29, 1985, Lecture Notes in Mathematics 218, Soubbaramayer and J. P. Boujot, eds., Springer-Verlag, 1985, pp. 603-607.

Spectral methods for the Euler equations: Chebyshev methods and shock-fitting, with D. Kopriva, M. D. Salas and T. A. Zang, AIAA Journal, 1985, 23(2): 234-240.

Spectral methods for Euler equations: Fourier methods and shock capturing, with D. Kopriva, M. D. Salas and T. A. Zang, AIAA Journal, 1985, 23(1): 64-70.

Spectral multigrid methods for Dirichlet problems, with T. Phillips and T. A. Zang, in Multigrid Methods for Integral and Differential Equations, H. Horstein and D. Paddon, eds., Oxford University Press, 1985, pp. 231-252.

Spectral multigrid methods with applications to transonic potential flow, with C. L. Streett and T. A. Zang, J. Comp. Physics, 1985, 57(1): 43-76.

Spectral methods for inviscid, compressible flows, with M. D. Salas and T. A. Zang, Advances in Computational Transonics, W. G. Habashi, Ed., Pineridge Press, 1985, pp. 875-912.

Iterative spectral methods and spectral methods for compressible flows, with T. A. Zang, in Spectral Methods for Partial Differential Equations, R. G. Voigt, D. Gottlieb, M. Y. Hussaini, eds., SIAM, Philadelphia, 1984, pp. 119-140.

Spectral methods for solution of boundary layer equations, with C. Streett and T. A. Zang, AIAA Paper 84-0170, 22nd Aerospace Sciences Meeting, Reno, Nevada, January 1984.

Spectral methods for partial differential equation, with C. L. Streett and T. A. Zang, Transactions of The First Army Conference on Applied Mathematics and Computing, ARO Report 84-1, 1984, pp. 883-925.

Spectral multigrid methods for elliptic equations II, with T. A. Zang and Y. S. Wong, J. Comp. Physics, 1984, 54(3): 489-507.

Numerical Computations of Turbulence Amplification in Shock Wave Interaction, with T.A. Zang and D.M. Bushnell, AIAA J., January 1984, 22(1): 13-21.

Pseudospectral Calculation of Shock-Turbulence Interactions, with T.A. Zang and D.A. Kopriva, Proc. of Numerical Methods Conference, C. Taylor, J.A. Johnson, W.R. Smith (eds.), Pineridge Press, Swansea, United Kingdom, 1984, pp. 210-221.

Theory and Applications of Spectral Methods, with D. Gottlieb and S.A. Orszag, Spectral Methods for Partial Differential Equations, R.G. Voight, D. Gottlieb, M.Y. Hussaini (eds.), SIAM-CBMS Series, 1984, pp. 1-54.

Pseudospectral solutions of two-dimensional gas dynamic problems, with D. A. Kopriva, T. A. Zang and M. D. Salas, Fifth GAMM - Conference on Numerical Methods in Fluid Dynamics, M. Pandolfi and R. Piva, eds., 1983, Friedr. Vieweg and Son, 1984, pp. 185-192.

Viscous, Resistive MHD Stability Computed by Spectral Techniques, with R.B. Dahlburg, T.A. Zang, and D.C. Montgomery, Proc. Nat. Acad. Sci., September 1983, 80: 5798-5802.

Navier-Stokes Solution of the CYBER-203 by a Pseudospectral Technique, with J.J. Lambiotte, S. Bokhari and S.A. Orszag, 10th IMACS World Congress on System Simulation and Scientific Computation, Vol. 1, August 8-13, 1982, Montreal, Canada, pp. 305-307.

Accurate Numerical Solution on Compressible, Linear Stability Equations, with M.R. Malik and S. Chuang, J. of Applied Mathematics and Physics (ZAMP), Vol. 33, March, 1982, pp.189-201.

Spectral Multi-Grid Methods for Elliptic Equations, with T.A. Zang and Y.S. Wong, J. Computational Physics, 1982, 48(3): 485-501.

Fast Orthogonal Derivatives on the STAR, with S. Bokhari and S. Orszag, Comput. Math Appl., 1982, 8(5): 367-377.

Shock-Fitted Euler Solutions to Shock-Vortex Interactions, with T.A. Zang and M.D. Salas, Lecture Notes in Physics, No. 170, E.Krause (ed.), Springer-Verlag, 1982, Proc of the 8th Intl. Conf. on Numerical Methods in Fluid Dynamics, Aachen, Germany, pp. 461-467.

Mixed Spectral Finite Difference Approximations for Slightly Viscous Flows, with T.A. Zang, Proc. of the 7th International Conference on Numerical Methods in Fluid Dynamics, Stanford, California, Lecture Notes in Physics, 1981, W. Reynolds and R. MacCormack (eds.), Springer-Verlag.

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