Spectral Element and DG Methods

Z. Wang, S. Dong, M.S. Triantatfyllou, Y. Constantinides, G.E. Karniadakis, “A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio”, Journal of Computational Physics 397, 108832, 2019.
Z. Wang, S. Dong, M.S. Triantatfyllou, Y. Constantinides, G.E. Karniadakis, “A spectral-element/Fourier smoothed profile method for large-eddy simulations of complex VIV problems”, Computers & Fluids 172,84-96, 2019.
Z. Zhang, W. Deng, G. E. Karniadakis, “A Riesz Basis Galerkin Method for the Tempered Fractional Laplacian.” SIAM J. Numer. Anal., 56(5), 3010-3039.
Z. Wang, S. Triantafyllou, Y. Constantinides, G. E. Karniadakis, “A spectral-element/Fournier smoothed profile method for large-eddy simulations of complex VIV problems.” Comp. Fluids, 172, 84-96, 2018.
X. Zhen, G. E. Karniadakis, “A phase-field/ALE method for simulating fluid-structure interactions in two-phase flow.” Comput. Methods Appl. Mech. Engrg. 309, 19-40,2016.
X. Zheng, H. Babaee, S. Dong, C. Chryssotomidis, and G.E. Karniadakis, “A phase-ﬁeld method for 3D simulation of two-phase heat transfer.” Int. J. of Heat and Mass Transfer, 82, 282-298, 2015.
S. Dong, G. E. Karniadakis, C. Chryssostomidis, “A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains.” J. Comput. Phys. 261, 83-105, 2014.
Y. Yue*, H. Baek* and G.E. Karniadakis, “Generalized ﬁctitious methods for ﬂuid-structure interactions: Analysis and simulations.” J. Comp. Phys. 245, 317-346, 2013.
H. Baek* and G.E. Karniadakis, “A convergence study of a new partitioned ﬂuid-structure interaction algorithm based on ﬁctitious mass and damping.” J. Comp. Phys. 231(2), 629-652, 2012.
B. Yildirim* and G.E. Karniadakis, “A hybrid spectral/DG method for solving the phase-averaged ocean wave equation: Algorithm and validation.” J. Comp. Phys. 231, 4921-4953, 2012.
Y. Yue*, H. Baek*, M.L. Bittencourt and G.E. Karniadakis, “Mixed spectral/hp element formulation for nonlinear elasticity.” Comput. Methods Appl. Mech. Engrg. 213-216, 42-57, 2012.
H. Baek* and G.E. Karniadakis, “Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations.” J. Comp. Phys. 230, 4384-4402, 2011.
L. Grinberg, G. E. Karniadakis, “Extrapolation-based acceleration of iterative solvers: Application to simulation of 3D flows.” Commun. Comput. Phys. 9(3), 607-626, 2011.
X. Luo*, A. Beskok and G.E. Karniadakis, “Modeling electrokinetic ﬂows by the smoothed proﬁle method.” J. Comp. Phys. 229, 3828-3847, 2010.
L. Grinberg, D. Pekorovsky, S. Sherwin, G. E. Karniadakis, “Parallel performance of the coarse space linear vertex solver and low energy basis preconditioner for spectral/hp elements.” Parallel Computing, 35(5), 284-304, 2009.
X. Luo, M. R. Maxey, G. E. Karniadakis, “Smoothed profile method for particulate flows: Error analysis and simulation.” J. Comp. Phys. 228, 1750-1769, 2009.
D. Liu, E. E. Keaveny, M. R. Maxey, G. E. Karniadakis, “Force coupling methods for flows with ellipsoidal particles.” J. Comp. Phys. 228(10), 3559-3581, 2009.
L. Grinberg* and G.E. Karniadakis, “Hierarchical spectral basis and Galerkin formulation using barycentric quadrature grids in triangular elements.” J. Engrg Math. 56(3), 289-306, 2007.
R.M. Kirby*, Z. Yosibash and G.E. Karniadakis, “Towards stable coupling methods for high-order discretization of ﬂuid-structure interaction: Algorithms and observations.” J. Comp. Phys. 223, 489-518, 2007.
X. Wan* and G.E. Karniadakis, “A sharp error estimate for the fast Gauss transform.” J. Comp. Phys. 219, 7-12, 2006
G. Lin, G. E. Karniadakis, ”A discontinuous Galerkin method for two-temperature plasmas.” Comput. Methods Appl. Mech. Engrg. 195, 3504-3527, 2006.
D. Xiu, S. J. Sherwin, S. Dong, G. E. Karniadakis, ”Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows.” J. Sci. Comp. 25(1), 323-346, 2005.
R. M. Kirby, G. E. Karniadakis, ”Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems.” J. Sci. Comp. 22-23, 385-411, Jan. 2005.
S. Dong, D. Liu, M. R. Maxey, G. E. Karniadakis, “Spectral distributed Lagrange multiplier (DLM) method: Algorithm and benchmark test s.” J. Comp. Phys. 195(2), 695-717, 2004.
R. M Kirby, G. E. Karniadakis, ”Spectral element and hp methods.” Encyclopedia of Computational Mechanics,” eds. E. Stein, R. de Borst, T. Hughes, John Wiley & Sons, 2004.
R. M. Kirby, G. E. Karniadakis, ”De-aliasing on non-uniform girds: algorithms and applications.” J. Comp. Phys. 91, 249-264, 2003.
Z. Yosibash, R. M. Kirby, K. Myers, B. Szabo, G. E. Karniadakis,”High-order finite elements for fluid structure interaction problems.” 44th AIAA/ASME/ASCE/AHS Structure, Structural Dynamics, and Materials Conference, Norfolk, VA, Apr. 7-10, 2003.
X. Ma, V. Symeonidis, G. E. Karniadakis, ”A spectral vanishing viscosity method for stabilizing viscoelastic flows.” J. Non-Newtonian Fluid Mech. 115, 125-155, 2003.
R. M. Kirby, G. E. Karniadakis, ”Coarse resolution turbulence simulations using SVV-LES.” J. Fluids Engn. 177, 133, 2002.
G. E. Karniadakis, S. J. Sherwin, ”Spectral/hp Element Methods for CFD.” Oxford University Press, March 1999. (Note: first monograph in this field); Second ed. Oxford 2005.
J. Xu, D. Xiu, G. E. Karniadakis, “A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations.” J. Sci. Comp. 17(1-4), 585-597, 2002.
C. Evangelinos*, D. Lucor*, C.-H. Su and G.E. Karniadakis, “Flow-induced vibrations of non-linear cables, Part I: Models and Algorithms.” Int. J. Num. Meth. Engrg. 55, 535-556, 2002.
R. M. Kirby, G. E. Karniadakis, ”Under-resolution and diagnostics in turbulent simulations of Complex-Geometry Flows.” Turbulent Flow Computations, Kluwer, 2002.
R.M. Kirby*, G.E. Karniadakis, O. Mikulchenko and K. Mayaram, “An integrated simulator for coupled domain problems in MEMS.” J. Microelectromechanical Systems, 10(3), 379-399, 2001.
D. Xiu, G. E. Karniadakis, ”A semi-Lagrangian high-order method for Navier-Stokes equations.” J. Comp. Phys. 172, 658-684, 2001.
I. Pivkin, R. M. Kirby, G. E. Karniadakis, ”High-order discontinuous Galerkin methods: Simulation of COIL flows.” Proc. Third AFOSR DNS/LES Conference, 2001.
G. Lin, G. E. Karniadakis, ”A high-order discontinuous Galerkin method for modeling micro pulsed plasma thrusters.” Proc. International Electric Propulsion Conference, Pasadena, CA, 2001.
G. S. Karamanos, G. E. Karniadakis, ”A spectral vanishing viscosity method for large-eddy simulations.” J. Comp. Phys. 162, 22-50, 2000.
”Discontinuous Galerkin Methods: Theory Computation and Applications.” (eds. B. Cockburn, G. E. Karniadakis, C.-W. Shu), Springer-Verlag, Feb., 2000.
I. Lomtev, R. M. Kirby, G. E. Karniadakis, ”A discontinuous Galerkin method in moving domains.” In Proc. of Discontinuous Galerkin Methods: Theory, Computation and Applications, eds. Cockburn et al., Springer-Verlag, NY, 1999.
I. Lomtev, R. M. Kirby, G. E. Karniadakis, ”DNS for flow past a 3D flexible wing.” eds. D. Knight and L. Sakell. Proc. of Second AFOSR Conference, Rutgers, Kluwer, June 7-9, 1999.
R. M. Kirby, T. C. Warburton, S. J. Sherwin, A. Beskok, G. E. Karniadakis, ‘‘The Nektar Code: Dynamic simulations without remeshing.” Proc. 2nd International Conference on Computational Technologies for Fluid/Thermal/Chemical Systems with Industrial Applications, August 1-5, 1999.
T. C. Warburton, G. E. Karniadakis, ”A discontinuous Galerkin method for the viscous MHD equations.” J. Comp. Phys. 152, 608-641, 1999.
T. C. Warburton, I. Lomtev, Y. Du, S. J. Sherwin, G. E. Karniadakis, ”Galerkin and discontinuous Galerkin spectral/hp methods.” Comp. Meth. Appl. Mech. Engr. 175, 343-359, 1999.
”Spectral, Spectral Element and hp Methods for CFD.” Guest editor of Comp. Meth. App. Mech. Engr. (co-eds, M. Ainsworth, C. Bernardi), vol. 175.
R. M. Kirby, T. C. Warburton, I. Lomtev, G. E. Karniadakis, ”A discontinuous Galerkin spectral/hp method on hybrid grids.” J. Appl. Num. Math. 33, 393-405, 1999.
J. Trujillo, G. E. Karniadakis, ”A penalty method for the vorticity-velocity formulation.” J. Comp. Phys. 149, 32-58, 1999.
T. C. Warburton, S. J. Sherwin, G. E. Karniadakis, ”Basis functions for triangular and quadrilateral high-order elements.” SIAM J. Sci. Comp. 20(5), 1671-1695, 1999.
I. Lomtev, G. E. Karniadakis, ”A discontinuous Galerkin method for the Navier-Stokes equations.” Int. J. Num. Meth. Fluids. 29, 587-603, 1999.
G. E. Karniadakis, ”Simulating turbulence in complex geometries.” Fluid Dynamics Research. 24 (6), 343-362, 1999.
I. Lomtev, R. M. Kirby, G. E. Karniadakis, “A discontinuous Galerkin ALE method for compressible viscous flows in moving domians.” J. Comp. Phys. 155,128-159, 1999.
T. C. Warburton, I. Lomtev, R. M. Kirby, G. E. Karniadakis, ‘A discontinuous galerkin method for the Navier Stokes equations.” Proc. Tenth International Conference on Finite Elements in Fluids, p. 604, eds. M. Hafez, J.C. Heirich, Tucson, AZ, Jan. 5-8, 1998.
I. Lomtev, C. B. Quillen, G. E. Karniadakis, ”Spectral/hp methods for viscous compressible flows on unstructured 2D meshes.” J. Comp. Phys. 144, 325-357, 1998.
S. J. Sherwin, T. C. Warburton, G. E. Karniadakis, ”Spectral/hp methods for elliptic problems on hybrid grids.” Contemporary Mathematics, 218, 191-215, 1998.
G. E. Karniadakis, R. D. Henderson, ”Spectral Element Methods for Incompressible Flows.” Chapter 29, Handbook of Fluid Dynamics, ed. R.W. Johnson, CRC Press, 1998.
I. Lomtev, G. E. Karniadakis, ”A discontinuous spectral/hp element Galerkin method for the Navier-Stokes equations on unstructured grids.” Proc. IMACS WC’97, Berlin, Germany, 1997.
I. Lomtev, G. E. Karniadakis, ”Simulations of viscous supersonic flows on unstructured h-p meshes.” AIAA 97-0754, 35th Aerospace Sciences Meeting, Reno, NV, 1997.
T. C. Warburton, G. E. Karniadakis, ”Spectral simulations of flow past a cylinder close to a free surface.” FEDSM97-3689, ASME Fluids Engineering Division Summer Meeting, Vancouver, BC. 1997.
S. J. Sherwin, G. E. Karniadakis, ”Tetrahedral hp finite elements: Algorithms and flow simulations.” J. Comp. Phys. 124, 14, 1996.
D. Pathria, G. E. Karniadakis, ”Spectral element methods for elliptic problems in non-smooth domains.” J. Comp. Phys. 122, 83, 1995.
S. J. Sherwin, G. E. Karniadakis, ”A triangular spectral element method; Applications to the incompressible Navier-Stokes equations.” Comp. Meth. Appl. Mech. Engr. 123, 189, 1995.
S. J. Sherwin, G. E. Karniadakis, ”A new triangular and tetrahedral basis for high-order finite element methods.’‘ Int. J. Num. Meth. Engn. 38, 3775, 1995.
R. D. Henderson, G. E. Karniadakis, ”Unstructured spectral element methods for simulation of turbulent flows.” J. Comp. Phys. 122, 191, 1995.
S. J. Sherwin, G. E. Karniadakis, ”Triangular and tetrahedral spectral elements.” ICOSAHOM’95, Houston, TX, June 5-9, 1995.
T. C. Warburton, S. J. Sherwin, G. E. Karniadakis, ”Unstructured hp/spectral elements: Connectivity and optimal ordering.” Int. Conf. on Comp. Engn. Science, Mauna Lani, HI, July 30-Aug. 3, 1995.
T. C. Warburton, S. J. Sherwin, G. E. Karniadakis, ”Hierarchical refinement using spectral/hp triangles and prisms.” Sixth Int. Symp. on CFD, Lake Tahoe, NV, Sept. 4-8, 1995
S. J. Sherwin, G. E. Karniadakis, ”Adaptive hp finite elements on unstructured meshes.” IX Int. Conf. on Finite Elements in Fluids: New Trends and Applications, Venice, IT, Oct. 15-21, 1995.
S. J. Sherwin, G. E. Karniadakis, ”Tetrahedral spectral elements for CFD.” Proc. 14th Int. Conf. Num. Meth. Fluid Dynamics, Bangalore, India, July 11-15, 1994.
S. J. Sherwin, G. E. Karniadakis, ”A triangular spectral element method: Algorithms and flow applications.” Computational Fluid Dynamics ’94, p. 62, John Wiley & Sons, 1994.
J. Giannakouros, G. E. Karniadakis, ”A spectral element-FCT method for the compressible Euler equations.” J. Comp. Phys. 115, 65, 1994.
J. Trujillo, G. E. Karniadakis, ”A spectral element velocity-vorticity algorithm for the incompressible Navier-Stokes equations.” Proc. 5th Int. Symp. on CFD, Sendai, Japan, 1993.
R. D. Henderson, G. E. Karniadakis, ”Unstructured spectral element methods for the incompressible Navier-Stokes equations.” Proc. Finite Elements in Fluids: New Trends and Applications,” eds. K. Morgan, E. Onate, J. Periaux, J. Peraire and O. C. Zienkewicz, Pineridge Press, 1993.
G. E. Karniadakis, S. A. Orszag, ”Some novel aspects of spectral methods,” Algorithmic Trends in Computational Fluid Dynamics.” eds. M. Y. Hussaini, A. Kumar, M. D. Salas, p. 245, Springer-Verlag, 1993.
G. E. Karniadakis, S. A. Orszag, E. M. Ronquist, A. T. Patera, ”Spectral element and lattice gas methods for incompressible fluid dynamics.” Incompressible Fluid Dynamics, Ch. 8, eds. M. D. Gunzburger, R. A. Nicolaides, Cambridge University Press, 1993.
D. Sidilkover, G. E. Karniadakis, ”Non-oscillatory spectral element Chebyshev method for shock wave calculations.” J. Comp. Phys. 107, 10-22, 1993.
J. Giannakouros, D. Sidilkover, G. E. Karniadakis, ”Spectral element-FCT method for the one- and two-dimensional compressible Euler equations.” Comp. Meth. Appl. Mech. Engr. 116, 113, 1994.
G. E. Karniadakis, M. Israeli, S. A. Orszag, ”High-order splitting methods for the incompressible Navier-Stokes equations.” J. Comp. Phys. 97, 414, 1991.
R. D. Henderson, G. E. Karniadakis, ”Hybrid spectral element-low order methods for incompressible flows.” J. Sci. Comp. 6(2), 79, 1991.
D. Pathria, G. E. Karniadakis, ”Dynamic generation of spectral element meshes through wavelet analysis.” USA-French Workshop on Wavelets and Turbulence, Princeton, 1991 (unpublished).
J. Giannakouros, G. E. Karniadakis, ”Spectral element-FCT method for scalar hyperbolic laws.” Proc. 3rd Int. Conf. on Hyperb. Problems, 1, 446, 1990 (also in Int. J. Num. Meth. Fluids, 14, p. 707, 1992).
J. Giannakouros, D. Sidilkover, G. E. Karniadakis, ”Hybrid spectral element methods for hyperbolic systems of conservation laws.” Proc. Fourth Int. Conf. on Hyperb. Problems, Taormina, IT, April, 1992.
R. D. Henderson, G. E. Karniadakis, ”Hybrid spectral element methods for flows over rough walls.” Proc. 5th Conf. on Domain Decomposition Methods, SIAM, 1991.
D. Sidilkover, J. Giannakouros, G. E. Karniadakis, ”Hybrid spectral element methods for hyperbolic conservation laws.” Proc. Ninth GAMM Conf. on Num. Meth. in Fluid Mech. Vieweg Verlag, 1991.
G. E. Karniadakis, ‘‘Spectral element-Fourier methods for incompressible turbulent flows.” Comp. Meth. Appl. Mech. Engr. 80, 362, 1990.
A. G. Tomboulides, M. Israeli, G. E. Karniadakis, ”Efficient removal of boundary- divergence errors in time-splitting methods.” J. Sci. Comp. 4, 291, 1989.
G. E. Karniadakis, ”Spectral element simulations of laminar and turbulent flows in complex geometries.” Appl. Num. Math. 6, 85-105, 1989.
C. Begue, C. Bernardi, N. Debit, Y. Maday, G. E. Karniadakis, A. T. Patera, ”Nonconforming spectral element-finite element approximations for the Navier-Stokes equations.” Proc. 8th Int. Conf. on Comp. Methods in Applied Science and Engineering, Versailles, France, 1987, also in C.M.A.M.E. 75, 109, 1989.
Y. Maday, A. T. Patera, G. E. Karniadakis, ”Spectral and finite element approximation for the unsteady incompressible Euler equations.” Notes aux Reudus de l’Academie des Sciences, Paris, France, 1987.
E. T. Bullister, G. E. Karniadakis, E. M. Ronquist, A. T. Patera, ”Solutions of the unsteady Navier-Stokes equations by spectral element methods.” Proc. 6th Int. Symp. on Finite Element Methods in Flow Problems, Antibes, France, 1986.
N.K. Ghaddar, G.E. Karniadakis & A.T. Patera, “A conservative isoparametric spectral element method for forced convection: Application to fully developed ﬂow in periodic geometries.” Num. Heat Transfer, 9, 277, 1986.
G. E. Karniadakis, E. T. Bullister, A. T. Patera, ”A spectral element method for solution of two- and three-dimensional time-dependent incompressible Navier-Stokes equations.” Proc. Europe-U.S. Conf. on Finite Element Methods for Nonlinear Problems, Springer-Verlag, p. 803, 1985.