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Volumn 225, Issue 2, 2007, Pages 1753-1781

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes

Author keywords

Discontinuous Galerkin finite element method (DGFEM); High order; Implicit explicit (IMEX) method; Navier Stokes equations

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; GALERKIN METHODS; NUMERICAL METHODS; RUNGE KUTTA METHODS; STIFFNESS;

EID: 34547533181     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.02.021     Document Type: Article
Times cited : (142)

References (44)
  • 3
    • 0031269714 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
    • Ascher U.M., Ruuth S.J., and Spiteri R.J. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25 (1997) 151-167
    • (1997) Appl. Numer. Math. , vol.25 , pp. 151-167
    • Ascher, U.M.1    Ruuth, S.J.2    Spiteri, R.J.3
  • 4
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time-dependent partial differential equations
    • Ascher U.M., Ruuth S.J., and Wetton B.T.R. Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32 (1995) 797-823
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 5
    • 48749141209 scopus 로고
    • Adaptive mesh refinement for hyperbolic partial differential equations
    • Berger M.J., and Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53 (1984) 484512
    • (1984) J. Comput. Phys. , vol.53 , pp. 484512
    • Berger, M.J.1    Oliger, J.2
  • 6
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267-279
    • (1997) J. Comput. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 8
    • 0035370920 scopus 로고    scopus 로고
    • Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations
    • Calvo M.P., de Frutos J., and Novo J. Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations. Appl. Numer. Math. 37 4 (2001) 535-549
    • (2001) Appl. Numer. Math. , vol.37 , Issue.4 , pp. 535-549
    • Calvo, M.P.1    de Frutos, J.2    Novo, J.3
  • 9
    • 85190759091 scopus 로고    scopus 로고
    • M.H. Carpenter, C.A. Kennedy, Fourth-Order 2N-Storage Runge-Kutta Schemes, NASA-TM-109112, 1994, pp. 1-24.
  • 10
    • 0002718851 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for convection-dominated problems
    • High-Order Methods for Computational Physics. Barth T.J., and Deconinck H. (Eds), Springer, Berlin
    • Cockburn B. Discontinuous Galerkin methods for convection-dominated problems. In: Barth T.J., and Deconinck H. (Eds). High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering vol. 9 (1999), Springer, Berlin 69-224
    • (1999) Lecture Notes in Computational Science and Engineering , vol.9 , pp. 69-224
    • Cockburn, B.1
  • 11
    • 0012095124 scopus 로고    scopus 로고
    • Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds), Springer Computing 16 (2001) 173-261
    • In: Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds). Discontinuous Galerkin Methods: Theory, Computation and Applications. Lecture Notes in Computational Science and Engineering vol. 11 (2000), Springer Computing 16 (2001) 173-261
    • (2000) Lecture Notes in Computational Science and Engineering , vol.11
  • 12
    • 0035683345 scopus 로고    scopus 로고
    • High resolution schemes for conservation laws with locally varying time steps
    • Dawson C.N., and Kirby R. High resolution schemes for conservation laws with locally varying time steps. SIAM J. Sci. Comput. 22 (2001) 22562281
    • (2001) SIAM J. Sci. Comput. , vol.22 , pp. 22562281
    • Dawson, C.N.1    Kirby, R.2
  • 13
    • 85190790489 scopus 로고    scopus 로고
    • T.A. Driscoll, A composite Runge-Kutta method for the spectral solution of semilinear PDE, 2001, unpublished.
  • 14
    • 0026371189 scopus 로고
    • Spectral methods on triangles and other domains
    • Dubiner M. Spectral methods on triangles and other domains. J. Sci. Comput. 6 (1991) 345-390
    • (1991) J. Sci. Comput. , vol.6 , pp. 345-390
    • Dubiner, M.1
  • 16
    • 0031273702 scopus 로고    scopus 로고
    • Numerical solution of viscoplastic constitutive equations with internal state variables, Part I: Algorithms and implementation
    • Fritzen P., and Wittekindt J. Numerical solution of viscoplastic constitutive equations with internal state variables, Part I: Algorithms and implementation. Math. Meth. Appl. Sci. 20 16 (1997) 1411-1425
    • (1997) Math. Meth. Appl. Sci. , vol.20 , Issue.16 , pp. 1411-1425
    • Fritzen, P.1    Wittekindt, J.2
  • 17
  • 18
    • 0026283488 scopus 로고
    • Control theoretic techniques for stepsize selection in Runge-Kutta methods
    • Gustafsson K. Control theoretic techniques for stepsize selection in Runge-Kutta methods. ACM Trans. Math. Soft. 17 4 (1991) 533-554
    • (1991) ACM Trans. Math. Soft. , vol.17 , Issue.4 , pp. 533-554
    • Gustafsson, K.1
  • 19
    • 0028737039 scopus 로고
    • Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods
    • Gustafsson K. Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Trans. Math. Soft. 20 4 (1994) 496-517
    • (1994) ACM Trans. Math. Soft. , vol.20 , Issue.4 , pp. 496-517
    • Gustafsson, K.1
  • 20
    • 0031129195 scopus 로고    scopus 로고
    • A stable penalty method for the compressible Navier-Stokes equations: II. One-dimensional domain decomposition schemes
    • Hesthaven J.S. A stable penalty method for the compressible Navier-Stokes equations: II. One-dimensional domain decomposition schemes. SIAM J. Sci. Comput. 18 3 (1997) 658-685
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.3 , pp. 658-685
    • Hesthaven, J.S.1
  • 21
    • 0000185847 scopus 로고    scopus 로고
    • From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex
    • Hesthaven J.S. From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J. Numer. Anal. 35 2 (1998) 655-676
    • (1998) SIAM J. Numer. Anal. , vol.35 , Issue.2 , pp. 655-676
    • Hesthaven, J.S.1
  • 22
    • 0036740992 scopus 로고    scopus 로고
    • Nodal high-order methods on unstructured grids I: Time-domain solution of Maxwell's equations
    • Hesthaven J.S., and Warburton T. Nodal high-order methods on unstructured grids I: Time-domain solution of Maxwell's equations. J. Comput. Phys. 181 (2002) 186-221
    • (2002) J. Comput. Phys. , vol.181 , pp. 186-221
    • Hesthaven, J.S.1    Warburton, T.2
  • 23
    • 1942424124 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for the time-domain Maxwell's equations: An introduction
    • Hesthaven J.S., and Warburton T. Discontinuous Galerkin methods for the time-domain Maxwell's equations: An introduction. ACES Newsletter 19 (2004) 12-30
    • (2004) ACES Newsletter , vol.19 , pp. 12-30
    • Hesthaven, J.S.1    Warburton, T.2
  • 24
    • 85190773100 scopus 로고    scopus 로고
    • A. Kanevsky, High-order implicit-explicit Runge-Kutta time integration schemes and time-consistent filtering in spectral Methods, Ph.D. Thesis, Brown University, 2006, pp. 1-138.
  • 25
    • 33750976193 scopus 로고    scopus 로고
    • Idempotent filtering in spectral and spectral element methods
    • Kanevsky A., Carpenter M.H., and Hesthaven J.S. Idempotent filtering in spectral and spectral element methods. J. Comput. Phys. 220 1 (2006) 41-58
    • (2006) J. Comput. Phys. , vol.220 , Issue.1 , pp. 41-58
    • Kanevsky, A.1    Carpenter, M.H.2    Hesthaven, J.S.3
  • 27
    • 0037216570 scopus 로고    scopus 로고
    • Additive Runge-Kutta schemes for convection-diffusion-reaction equations
    • Kennedy C.A., and Carpenter M.H. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44 (2003) 139-181
    • (2003) Appl. Numer. Math. , vol.44 , pp. 139-181
    • Kennedy, C.A.1    Carpenter, M.H.2
  • 28
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: a survey of approaches and applications
    • Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2004) 357-397
    • (2004) J. Comput. Phys. , vol.193 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 29
    • 0001203562 scopus 로고    scopus 로고
    • Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow
    • Knoll D.A., and McHugh P.R. Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow. SIAM J. Sci. Comput. 19 (1998) 291-301
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 291-301
    • Knoll, D.A.1    McHugh, P.R.2
  • 30
    • 0002095317 scopus 로고
    • Two-variable analogues of the classical orthogonal polynomials
    • Askey R.A. (Ed), Academic Press, New York
    • Koornwinder T. Two-variable analogues of the classical orthogonal polynomials. In: Askey R.A. (Ed). Theory and Application of Special Functions (1975), Academic Press, New York 435-495
    • (1975) Theory and Application of Special Functions , pp. 435-495
    • Koornwinder, T.1
  • 33
    • 84966225456 scopus 로고
    • Numerical approximations to nonlinear conservation laws with locally varying time and space grids
    • Osher S., and Sanders R. Numerical approximations to nonlinear conservation laws with locally varying time and space grids. Math. Comp. 41 (1983) 321336
    • (1983) Math. Comp. , vol.41 , pp. 321336
    • Osher, S.1    Sanders, R.2
  • 34
    • 48549109395 scopus 로고
    • Element method for fluid dynamics: laminar flow in a channel expansion
    • Patera A.T., and Spectral A. Element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54 (1984) 468-488
    • (1984) J. Comput. Phys. , vol.54 , pp. 468-488
    • Patera, A.T.1    Spectral, A.2
  • 35
    • 33846453567 scopus 로고    scopus 로고
    • Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
    • Piperno S. Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems. ESAIM:M2AN 40 (2006) 815-841
    • (2006) ESAIM:M2AN , vol.40 , pp. 815-841
    • Piperno, S.1
  • 36
    • 0001655705 scopus 로고
    • Sur une famille de polynomes deux variables orthogonaux dans un triangle
    • Proriol J. Sur une famille de polynomes deux variables orthogonaux dans un triangle. C. R. Acad. Sci. Paris 257 (1957) 2459-2461
    • (1957) C. R. Acad. Sci. Paris , vol.257 , pp. 2459-2461
    • Proriol, J.1
  • 37
    • 85190792753 scopus 로고    scopus 로고
    • W.H. Reed, T.R. Hill, Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Laboratory Report LA-UR-73-479, 1973.
  • 39
    • 0036441379 scopus 로고    scopus 로고
    • Automatic control and adaptive time-stepping, Numerical methods for ordinary differential equations (Auckland, 2001)
    • Soderlind G. Automatic control and adaptive time-stepping, Numerical methods for ordinary differential equations (Auckland, 2001). Numer. Algorithms 31 1-4 (2002) 281-310
    • (2002) Numer. Algorithms , vol.31 , Issue.1-4 , pp. 281-310
    • Soderlind, G.1
  • 40
    • 4544281285 scopus 로고    scopus 로고
    • Moving mesh methods with locally varying time steps
    • Tan Z., Zhang Z., Huang Y., and Tang T. Moving mesh methods with locally varying time steps. J. Comput. Phys. 200 (2004) 347-367
    • (2004) J. Comput. Phys. , vol.200 , pp. 347-367
    • Tan, Z.1    Zhang, Z.2    Huang, Y.3    Tang, T.4
  • 41
    • 0024737429 scopus 로고
    • Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers
    • Williamson C.H.K. Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206 (1989) 579-627
    • (1989) J. Fluid Mech. , vol.206 , pp. 579-627
    • Williamson, C.H.K.1
  • 42
    • 0002255298 scopus 로고
    • Low-storage Runge-Kutta schemes
    • Williamson J.H. Low-storage Runge-Kutta schemes. J. Comput. Phys. 35 (1980) 48
    • (1980) J. Comput. Phys. , vol.35 , pp. 48
    • Williamson, J.H.1
  • 43
    • 85190757207 scopus 로고    scopus 로고
    • J.J.-I. Yoh, X. Zhong, Semi-implicit Runge-Kutta schemes for stiff multi-dimensional reacting flows, AIAA Paper 97-0803, AIAA, Aerospace Sciences Meeting and Exhibit, 35th, Reno, NV, January 6-9, 1997.
  • 44
    • 85190775887 scopus 로고    scopus 로고
    • X. Zhong, New high-order semi-implicit Runge-Kutta schemes for computing transient nonequilibrium hypersonic flows, AIAA Paper 95-2007, AIAA, Thermophysics Conference, 30th, San Diego, CA, June 19-22, 1995.


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