High-Order Numerical Methods

1. S. Dong, G.E. Karnidakis and 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.
   
   
2. L. Grinberg and G.E. Karniadakis, "Extrapolation-based acceleration of iterative solvers: Application to simulation of 3D flows," Commun. Comput. Phys., 9(3), 607-626, 2011.
3. L. Grinberg, D. Pekorovsky, S. Sherwin and G.E. Karniadakis, "Parallel performance of a low energy basis preconditioner for spectral/hp elements," Parallel Computing, 35(5), 284-304, 2009.

4. X. Luo, M.R. Maxey and G.E. Karniadakis, "Smoothed profile method for particulate flows: Error analysis and simulation, J. Comp. Phys. 228, 1750-1769, 2009.

5. D. Liu, E.E. Keaveny, M.R. Maxey and G.E. Karniadakis, "Force coupling methods for flows with ellipsoidal particles, J. Comp. Phys. 228(10), 3559-3581, 2009.

6. G. Lin and G.E. Karniadakis, ''A discontinuous Galerkin method for two-temperature plasmas,'' Comput. Methods Appl. Mech. Engrg., 195, 3504-3527, 2006.

7. D. Xiu, S.J. Sherwin, S. Dong and G.E. Karniadakis, ''Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows,'' J. Sci. Comp.25(1), 323-346, 2005.

8. R.M. Kirby and G.E. Karniadakis, ''Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems,'' J. Sci. Comp., vols. 22-23, numbers 1-3, pp. 385-411, January 2005.

9. S. Dong, D. Liu, M.R. Maxey and G.E. Karniadakis, "Spectral distributed multiplier (DLM) method: Algorithm and benchmark test, J. Comp. Phys., 195(2), 695-717 2004.

10. R.M Kirby and G.E. Karniadakis, ''Spectral element and hp methods,'' Encyclopedia of Computational Mechanics, edited by: E. Stein, R. de Borst, T. Hughes, John Wiley & Sons, 2004.

11. R.M. Kirby and G.E. Karniadakis, ''De-aliasing on non-uniform girds: algorithms and applications, J. Comp. Phys., 91, 249-264, 2003.

12. Z. Yosibash, R.M. Kirby, K. Myers, B. Szabo and G. Karniadakis,''High-order finite elements for fluid structure interaction problems,'' 44th AIAA/ASME/ASCE/AHS Structure, Structural Dynamics, and Materials Conference, April 7-10 2003, Norfolk, Virginia.

13. X. Ma, V. Symeonidis and G.E. Karniadakis, ''A spectral vanishing viscosity method for stabilizing viscoelastic flows,'' Journal of Non-Newtonian Fluid Mechanics, 115, 125-155, 2003.

14. R.M. Kirby and G.E. Karniadakis, ''Coarse resolution turbulence simulations using SVV-LES,'' J. Fluids Eng., 177, 133, 2002.

15. G.E. Karniadakis and S.J. Sherwin, ''Spectral/hp Element Methods for CFD,'' Oxford University Press, March 1999. (first monograph in this field); second edition, Oxford 2005.

16. J. Xu, D. Xiu and G.E. Karniadakis, A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations,'' J. Sci. Comp., 17(1-4), 585-597, 2002.

17. R.M. Kirby and G.E. Karniadakis, ''Under-resolution and diagnostics in turbulent simulations of Complex-Geometry Flows,'' Turbulent Flow Computations, Kluwer, 2002.

18. D. Xiu and G.E. Karniadakis, ''A semi-Lagrangian high-order method for Navier-Stokes equations,'' J. Comp. Phys., vol. 172, pp. 658-684, 2001.

19. I. Pivkin, R.M. Kirby and G.E. Karniadakis, ''High-order discontinuous Galerkin methods: Simulation of COIL flows,'' Proc. Third AFOSR DNS/LES Conference, 2001.

20. G. Lin and G.E. Karniadakis, ''A High-order discontinuous Galerkin method for modeling micro pulsed plasma thrusters,'' Proc. International Electric Propulsion Conference, Pasadena, CA, 2001.

21. G.S. Karamanos and G.E. Karniadakis, ''A spectral vanishing viscosity method for large-eddy simulations,'' J. Comp. Phys., vol. 162, pp. 22-50, 2000.

22. ''Discontinuous Galerkin Methods: Theory Computation and Applications,'' (editors: B. Cockburn, G.E. Karniadakis and C.-W. Shu), Springer-Verlag, February 2000.

23. I. Lomtev, R.M. Kirby and 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.

24. I. Lomtev, R.M. Kirby and G.E. Karniadakis, ''DNS for flow past a 3D flexible wing,'' Proc. of Second AFOSR Conference, Rutgers, June 7-9, 1999, published by Kluwer, eds. D. Knight and L. Sakell.

25. R.M. Kirby, T.C. Warburton, S.J. Sherwin, A. Beskok and 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.

26. T.C. Warburton and G.E. Karniadakis, ''A discontinuous Galerkin method for the viscous MHD equations,'' J. Comp. Phys., vol. 152, pp. 608-641, 1999.

27. T.C. Warburton, I. Lomtev, Y. Du, S.J. Sherwin, and G.E. Karniadakis, ''Galerkin and discontinuous Galerkin spectral/hp methods,'' Comp. Meth. Appl. Mech. Engr., vol. 175, pp. 343-359, 1999.

28. ''Spectral, Spectral Element and hp Methods for CFD,'' guest editor of Comp. Meth. App. Mech. Engr., (co-editors: M. Ainsworth and C. Bernardi), vol. 175.

29. R.M. Kirby, T.C. Warburton, I. Lomtev and G.E. Karniadakis, ''A discontinuous Galerkin spectral/hp method on hybrid grids,'' J. Appl. Num. Math., vol. 33, pp. 393-405, 1999.

30. J. Trujillo and G.E. Karniadakis, ''A penalty method for the vorticity-velocity formulation,'' J. Comp. Phys., vol. 149, pp. 32-58, 1999.

31. T.C. Warburton, S.J. Sherwin and G.E. Karniadakis, ''Basis functions for triangular and quadrilateral high-order elements,'' SIAM J. Scientific Computing, vol. 20(5), pp. 1671-1695, 1999.

32. I. Lomtev and G.E. Karniadakis, ''A discontinuous Galerkin method for the Navier-Stokes equations,'' Int. J. Num. Meth. Fluids, vol. 29, pp. 587-603, 1999.

33. G.E. Karniadakis, ''Simulating turbulence in complex geometries,'' Fluid Dynamics Research, vol. 24 (6), pp. 343-362, 1999.

34. T.C. Warburton, I. Lomtev, R.M. Kirby and G.E. Karniadakis, ''A discontinuous Galerkin method for the compressible Navier-Stokes equations on hybrid grids,'' Proc. Tenth International Conference on Finite Elements in Fluids, January 5-8, 1998, Tucson, Arizona, p. 604, Eds. M. Hafez and J.C. Heirich.

35. I. Lomtev, C.B. Quillen and G.E. Karniadakis, ''Spectral/hp methods for viscous compressible flows on unstructured 2D meshes,'' J. Comp. Phys., vol. 144, pp. 325-357, 1998.

36. S.J. Sherwin, T.C. Warburton and G.E. Karniadakis, ''Spectral/hp methods for elliptic problems on hybrid grids,'' Contemporary Mathematics, vol. 218, p. 191-215, 1998.

37. G.E. Karniadakis and R.D. Henderson, ''Spectral Element Methods for Incompressible Flows,'' chapter 29 in Handbook of Fluid Dynamics, edited by R.W. Johnson, CRC Press, 1998.

38. I. Lomtev and 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.

39. I. Lomtev and G.E. Karniadakis, ''Simulations of viscous supersonic flows on unstructured h-p meshes,'' AIAA 97-0754, 35th Aerospace Sciences Meeting, Reno, 1997.

40. T.C. Warburton and G.E. Karniadakis, ''Spectral simulations of flow past a cylinder close to a free surface,'' FEDSM97-3689, ASME Fluids Engineering Division Summer Meeting, Vancouver, 1997.

41. S.J. Sherwin and G.E. Karniadakis, ''Tetrahedral hp finite elements: Algorithms and flow simulations,'' J. Comp. Phys., vol. 124, p. 14, 1996.

42. D. Pathria and G.E. Karniadakis, ''Spectral element methods for elliptic problems in non-smooth domains,'' J. Comp. Phys., vol. 122, p. 83, 1995.

43. S.J. Sherwin and G.E. Karniadakis, ''A triangular spectral element method; Applications to the incompressible Navier-Stokes equations,'' Comp. Meth. Appl. Mech. Engr. vol. 123, p. 189, 1995.

44. S.J. Sherwin and G.E. Karniadakis, ''A new triangular and tetrahedral basis for high-order finite element methods,'' Int. J. Num. Meth. Eng., vol. 38, p. 3775, 1995.

45. R.D. Henderson and G.E. Karniadakis, ''Unstructured spectral element methods for simulation of turbulent flows,'' J. Comp. Phys., vol. 122 p. 191, 1995.

46. S.J. Sherwin and G.E. Karniadakis, ''Triangular and tetrahedral spectral elements,'' ICOSAHOM'95, June 5-9, 1995, Houston, TX.

47. T.C. Warburton, S.J. Sherwin and G.E. Karniadakis, ''Unstructured hp/spectral elements: Connectivity and optimal ordering,'' Int. Conf. on Comp. Engin. Science, July 30-August 3, 1995, Mauna Lani, Hawaii.

48. T.C. Warburton, S.J. Sherwin and G.E. Karniadakis, ''Hierarchical refinement using spectral/hp triangles and prisms,'' Sixth Int. Symp. on CFD, September 4-8, 1995, Lake Tahoe, Nevada.

49. S.J. Sherwin and G.E. Karniadakis, ''Adaptive hp finite elements on unstructured meshes,'' IX Int. Conf. on Finite Elements in Fluids: New Trends and Applications, October 15-21, 1995, Venice, Italy.

50. S.J. Sherwin and G.E. Karniadakis, ''Tetrahedral spectral elements for CFD,'' Proc. 14th Int. Conf. Num. Meth. Fluid Dynamics, July 11-15, 1994, Bangalore, India.

51. S.J. Sherwin and G.E. Karniadakis, ''A triangular spectral element method: Algorithms and flow applications,'' Computational Fluid Dynamics '94, p. 62, John Wiley & Sons, 1994.

52. J. Giannakouros and G.E. Karniadakis, ''A spectral element-FCT method for the compressible Euler equations,'' J. Comp. Phys., vol 115, p. 65, 1994.

53. J. Trujillo and G.E. Karniadakis, ''A spectral element velocity-vorticity algorithm for the incompressible Navier-Stokes equations,'' Proc. 5th Int. Symp. on CFD, Sendai Japan, 1993.

54. R.D. Henderson and G.E. Karniadakis, ''Unstructured spectral element methods for the incompressible Navier-Stokes equations,'' in 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.

55. G.E. Karniadakis and 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.

56. G.E. Karniadakis, S.A. Orszag, E.M. Ronquist and A.T. Patera, ''Spectral element and lattice gas methods for incompressible fluid dynamics,'' chapter 8 in Incompressible Fluid Dynamics, eds. M.D. Gunzburger and R.A. Nicolaides, Cambridge University Press, 1993.

57. D. Sidilkover and G.E. Karniadakis, ''Non-oscillatory spectral element Chebyshev method for shock wave calculations,'' Proc. 5th Conf. on Domain Decomposition Methods, SIAM, 1991, also in J. Comp. Phys., vol. 107, p. 10, 1993.

58. J. Giannakouros, D. Sidilkover and G.E. Karniadakis, ''Spectral element-FCT method for the one- and two-dimensional Euler equations,'' Comp. Meth. Appl. Mech. Engr., vol. 116, p. 113, 1994; also in ICOSAHOM, p. 113, (eds. C. Bernardi and Y. Maday), North Holland, 1992.

59. G.E. Karniadakis, M. Israeli and S.A. Orszag, ''High-order splitting methods for the incompressible Navier-Stokes equations,'' J. Comp. Phys., vol. 97, p. 414, 1991.

60. R.D. Henderson and G.E. Karniadakis, ''Hybrid spectral element-low order methods for incompressible flows,'' J. Sci. Comp., vol. 6, No. 2, p. 79, 1991.

61. D. Pathria and G.E. Karniadakis, ''Dynamic generation of spectral element meshes through wavelet analysis,'' USA-French Workshop on Wavelets and Turbulence, Princeton, 1991 (unpublished).

62. J. Giannakouros and G.E. Karniadakis, ''Spectral element-FCT method for scalar hyperbolic laws,'' Proc. 3rd Int. Conf. on Hyperb. Problems, vol. 1, p. 446, 1990 (also in Int. J. Num. Meth. Fluids, 14, p.707, 1992).

63. J. Giannakouros, D. Sidilkover and G.E. Karniadakis, ''Hybrid spectral element methods for hyperbolic systems of conservation laws,'' Proc. Fourth Int. Conf. on Hyperb. problems, Taormina, Italy, April, 1992.

64. R.D. Henderson and G.E. Karniadakis, ''Hybrid spectral element methods for flows over rough walls,'' Proc. 5th Conf. on Domain Decomposition Methods, SIAM, 1991.

65. D. Sidilkover, J. Giannakouros and G.E. Karniadakis, ''Hybrid spectral element methods for hyperbolic conservation laws,'' Proc. Ninth GAMM Conf. on Num. Meth. in Fluid Mech., Vieweg Verlag, 1991.

66. G.E. Karniadakis, ''Spectral element-Fourier methods for incompressible turbulent flows,'' Comp. Meth. Appl. Mech. Engr., vol. 80, p. 362, 1990. (also in Proc. ICOSAHOM'89 Conf., Como, 1989).

67. A.G. Tomboulides, M. Israeli and G.E. Karniadakis, ''Efficient removal of boundary- divergence errors in time-splitting methods,'' J. Sci. Comp., vol. 4, p. 291, 1989.

68. G.E. Karniadakis, ''Spectral element simulations of laminar and turbulent flows in complex geometries,'' Appl. Num. Math., vol. 6, p. 85, 1989.

69. C. Begue, C. Bernardi, N. Debit, Y. Maday, G.E. Karniadakis and 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, Versaille, 1987, also in C.M.A.M.E., vol. 75, p. 109, 1989.

70. Y. Maday, A.T. Patera and G.E. Karniadakis, ''Spectral and finite element approximation for the unsteady incompressible Euler equations,'' Notes aux Reudus de l'Academie des Sciences, Paris, 1987, (invited).

71. E.T. Bullister, G.E. Karniadakis, E.M. Ronquist and 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, 1986.

72. G.E. Karniadakis, E.T. Bullister and 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.