메뉴 건너뛰기




Volumn 230, Issue 22, 2011, Pages 8028-8056

Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

Author keywords

Adaptive slope limiting; Advective transport; Discontinuous Galerkin; Dynamic p adaptivity; Dynamic p enrichment; Error analysis; Finite element; Hyperbolic PDE; RKDG; Shock capturing; Strong stability preserving (SSP); Total variation diminishing (TVD)

Indexed keywords

ERROR ANALYSIS; GALERKIN METHODS; RUNGE KUTTA METHODS; SLOPE STABILITY;

EID: 84860408394     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.07.009     Document Type: Article
Times cited : (27)

References (44)
  • 1
    • 0002677386 scopus 로고
    • On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
    • ISSN 0021-9991
    • Abgrall R. On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J. Comput. Phys. 1994, 114(1):45-58. ISSN 0021-9991. 10.1006/jcph.1994.1148.
    • (1994) J. Comput. Phys. , vol.114 , Issue.1 , pp. 45-58
    • Abgrall, R.1
  • 2
    • 0036149118 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for two-dimensional flow and transport in shallow water
    • ISSN 0309-1708. URL
    • Aizinger V., Dawson C. A discontinuous Galerkin method for two-dimensional flow and transport in shallow water. Adv. Water Res. 2002, 25(1):67-84. ISSN 0309-1708. URL http://www.sciencedirect.com/science/article/B6VCF-44PK3KB-5/2/51beaaea1191c299bcd3a0d40beca43d. 10.1016/S0309-1708(01)00019-7.
    • (2002) Adv. Water Res. , vol.25 , Issue.1 , pp. 67-84
    • Aizinger, V.1    Dawson, C.2
  • 3
    • 0002718850 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for elliptic problems
    • Springer, Berlin, Newport, RI, (1999), Discontinuous Galerkin methods
    • Arnold D.N., Brezzi F., Cockburn B., Marini D. Discontinuous Galerkin methods for elliptic problems. Lecture Notes Computer Science and Engineering 2000, vol. 11:89-101. Springer, Berlin, Newport, RI, (1999).
    • (2000) Lecture Notes Computer Science and Engineering , vol.11 , pp. 89-101
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, D.4
  • 4
    • 1542741325 scopus 로고    scopus 로고
    • Numerical problems in semiconductor simulation using the hydrodynamic model: a second-order finite difference scheme
    • ISSN 0021-9991
    • Ballestra L.V., Sacco R. Numerical problems in semiconductor simulation using the hydrodynamic model: a second-order finite difference scheme. J. Comput. Phys. 2004, 195(1):320-340. ISSN 0021-9991. 10.1016/j.jcp.2003.10.002.
    • (2004) J. Comput. Phys. , vol.195 , Issue.1 , pp. 320-340
    • Ballestra, L.V.1    Sacco, R.2
  • 5
    • 67649261504 scopus 로고    scopus 로고
    • Data structures and requirements for hp finite element software
    • ISSN 0098-3500. URL
    • Bangerth W., Kayser-Herold O. Data structures and requirements for hp finite element software. ACM Trans. Math. Softw. 2009, 36:4:1-4:31. ISSN 0098-3500. URL http://doi.acm.org/10.1145/1486525.1486529.
    • (2009) ACM Trans. Math. Softw. , vol.36
    • Bangerth, W.1    Kayser-Herold, O.2
  • 6
    • 0003827428 scopus 로고
    • The design and application of upwind schemes and unstructured meshes
    • Barth T., Jesperson D.C. The design and application of upwind schemes and unstructured meshes. AIAA paper 1989, 89(0366):1-12.
    • (1989) AIAA paper , vol.89 , Issue.366 , pp. 1-12
    • Barth, T.1    Jesperson, D.C.2
  • 7
    • 33749535785 scopus 로고
    • An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
    • ISSN 0021-9991. URL
    • Bell J.B., Dawson C.N., Shubin G.R. An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions. J. Comput. Phys. 1988, 74(1):1-24. ISSN 0021-9991. URL http://www.sciencedirect.com/science/article/B6WHY-4DD1T8P-N0/2/aba1bf519b0924a0a20968665aa37091. 10.1016/0021-9991(88)90065-4.
    • (1988) J. Comput. Phys. , vol.74 , Issue.1 , pp. 1-24
    • Bell, J.B.1    Dawson, C.N.2    Shubin, G.R.3
  • 8
    • 61849156279 scopus 로고    scopus 로고
    • A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations
    • ISSN 0045-7825
    • Bunya S., Kubatko E.J., Westerink J.J., Dawson C. A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations. Comput. Methods Appl. Mech. Engg. 2009, 198(17-20):1548-1562. ISSN 0045-7825. 10.1016/j.cma.2009.01.008.
    • (2009) Comput. Methods Appl. Mech. Engg. , vol.198 , Issue.17-20 , pp. 1548-1562
    • Bunya, S.1    Kubatko, E.J.2    Westerink, J.J.3    Dawson, C.4
  • 9
    • 11144330928 scopus 로고    scopus 로고
    • A dynamic p-adaptive discontinuous Galerkin method for viscous flow with shocks
    • ISSN 0045-7930
    • Burbeau A., Sagaut P. A dynamic p-adaptive discontinuous Galerkin method for viscous flow with shocks. Comput. Fluids 2005, 34(4-5):401-417. ISSN 0045-7930. 10.1016/j.compfluid.2003.04.002.
    • (2005) Comput. Fluids , vol.34 , Issue.4-5 , pp. 401-417
    • Burbeau, A.1    Sagaut, P.2
  • 10
    • 33947622505 scopus 로고    scopus 로고
    • Computing with hp-adaptive finite elements
    • Chapman & Hall/CRC, Boca Raton, FL, ISBN 978-1-58488-671-6; 1-58488-671-4. One and two dimensional elliptic and Maxwell problems, With 1 CD-ROM (UNIX)
    • Demkowicz L. Computing with hp-adaptive finite elements. Applied Mathematics and Nonlinear Science Series 2007, vol. 1. Chapman & Hall/CRC, Boca Raton, FL, ISBN 978-1-58488-671-6; 1-58488-671-4. One and two dimensional elliptic and Maxwell problems, With 1 CD-ROM (UNIX).
    • (2007) Applied Mathematics and Nonlinear Science Series , vol.1
    • Demkowicz, L.1
  • 11
    • 84888878160 scopus 로고    scopus 로고
    • A new discontinuous Petrov-Galerkin method with optimal test functions
    • Demkowicz L. A new discontinuous Petrov-Galerkin method with optimal test functions. Part V: solution of 1D Burgers and Navier-Stokes equations 2010, 34. http://www.ices.utexas.edu/media/reports/2010/1025.pdf.
    • (2010) Part V: solution of 1D Burgers and Navier-Stokes equations , pp. 34
    • Demkowicz, L.1
  • 12
    • 0003018067 scopus 로고
    • Triangle based adaptive stencils for the solution of hyperbolic conservation laws
    • ISSN 0021-9991.
    • Durlofsky L.J., Engquist B., Osher S. Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J. Comput. Phys. 1992, 98(1):64-73. ISSN 0021-9991. http://www.sciencedirect.com/science/article/B6WHY-4DD1P88-NW/2/14f5775efbf9049e31e12411e2e34238. 10.1016/0021-9991(92)90173-V.
    • (1992) J. Comput. Phys. , vol.98 , Issue.1 , pp. 64-73
    • Durlofsky, L.J.1    Engquist, B.2    Osher, S.3
  • 14
    • 66149134905 scopus 로고    scopus 로고
    • An improvement of classical slope limiters for high-order discontinuous Galerkin method
    • ISSN 0271-2091. URL
    • Ghostine R., Kesserwani G., Mosé R., Vazquez J., Ghenaim A. An improvement of classical slope limiters for high-order discontinuous Galerkin method. Int. J. Numer. Methods Fluids 2009, 59(4):423-442. ISSN 0271-2091. URL http://dx.doi.org/10.1002/fld.1823. 10.1002/fld.1823.
    • (2009) Int. J. Numer. Methods Fluids , vol.59 , Issue.4 , pp. 423-442
    • Ghostine, R.1    Kesserwani, G.2    Mosé, R.3    Vazquez, J.4    Ghenaim, A.5
  • 15
    • 77949324581 scopus 로고    scopus 로고
    • On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media
    • ISSN 0021-9991. URL
    • Godoy W.F., DesJardin P.E. On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media. J. Comput. Phys. 2010, 229(9):3189-3213. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2009.12.037. 10.1016/j.jcp.2009.12.037.
    • (2010) J. Comput. Phys. , vol.229 , Issue.9 , pp. 3189-3213
    • Godoy, W.F.1    DesJardin, P.E.2
  • 16
    • 10644264359 scopus 로고    scopus 로고
    • New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes
    • ISSN 0029-5981. URL
    • Hoteit H., Ackerer Ph., Mosé R., Erhel J., Philippe B. New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes. Int. J. Numer. Methods Eng. 2004, 61(14):2566-2593. ISSN 0029-5981. URL http://dx.doi.org/10.1002/nme.1172. 10.1002/nme.1172.
    • (2004) Int. J. Numer. Methods Eng. , vol.61 , Issue.14 , pp. 2566-2593
    • Hoteit, H.1    Ackerer, P.2    Mosé, R.3    Erhel, J.4    Philippe, B.5
  • 18
    • 33846813497 scopus 로고    scopus 로고
    • A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
    • ISSN 0021-9991. URL
    • Jin C., Xu K. A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation. J. Comput. Phys. 2007, 222(1):155-175. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2006.07.015. 10.1016/j.jcp.2006.07.015.
    • (2007) J. Comput. Phys. , vol.222 , Issue.1 , pp. 155-175
    • Jin, C.1    Xu, K.2
  • 19
    • 4944249121 scopus 로고    scopus 로고
    • Multilevel methods for discontinuous galerkin fem on locally refined meshes
    • ISSN 0045-7949. URL. Preconditioning methods: algorithms, applications and software environments
    • Kanschat G. Multilevel methods for discontinuous galerkin fem on locally refined meshes. Comput. Struct. 2004, 82(28):2437-2445. ISSN 0045-7949. URL http://www.sciencedirect.com/science/article/B6V28-4DBJGG5-4/2/5cb85d27cc196137146048cd3d9d4c33. Preconditioning methods: algorithms, applications and software environments. 10.1016/j.compstruc.2004.04.015.
    • (2004) Comput. Struct. , vol.82 , Issue.28 , pp. 2437-2445
    • Kanschat, G.1
  • 20
    • 33846598544 scopus 로고    scopus 로고
    • Hp discontinuous Galerkin methods for advection dominated problems in shallow water flow
    • ISSN 0045-7825.
    • Kubatko E.J., Westerink J.J., Dawson C. hp discontinuous Galerkin methods for advection dominated problems in shallow water flow. Comput. Methods Appl. Mech. Eng. 2006, 196(1-3):437-451. ISSN 0045-7825. http://www.sciencedirect.com/science/article/B6V29-4M1CYTM-1/2/6c45c85d20d17690046881a795b0b04d. 10.1016/j.cma.2006.05.002.
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.196 , Issue.1-3 , pp. 437-451
    • Kubatko, E.J.1    Westerink, J.J.2    Dawson, C.3
  • 21
    • 33847034771 scopus 로고    scopus 로고
    • Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations
    • ISSN 0021-9991. URL 2006.08.005
    • Kubatko E.J., Westerink J.J., Dawson C. Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations. J. Comput. Phys. 2007, 222(2):832-848. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2006.08.005. 10.1016/j.jcp.2006.08.005.
    • (2007) J. Comput. Phys. , vol.222 , Issue.2 , pp. 832-848
    • Kubatko, E.J.1    Westerink, J.J.2    Dawson, C.3
  • 22
    • 53349096400 scopus 로고    scopus 로고
    • Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
    • ISSN 0021-9991. URL.2008.07.026
    • Kubatko E.J., Dawson C., Westerink J.J. Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids. J. Comput. Phys. 2008, 227(23):9697-9710. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2008.07.026. 10.1016/j.jcp.2008.07.026.
    • (2008) J. Comput. Phys. , vol.227 , Issue.23 , pp. 9697-9710
    • Kubatko, E.J.1    Dawson, C.2    Westerink, J.J.3
  • 23
    • 63249134383 scopus 로고    scopus 로고
    • Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations
    • ISSN 0045-7825). URL. Advances in Simulation-Based Engineering Sciences - Honoring J. Tinsley Oden
    • Kubatko E.J., Bunya S., Dawson C., Westerink J.J. Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations. Comput. Methods Appl. Mech. Eng. 2009, 198(21-26):1766-1774. ISSN 0045-7825). URL http://www.sciencedirect.com/science/article/B6V29-4VDY7X4-1/2/36e49328fea4e4f751d689510b7e3b3f. Advances in Simulation-Based Engineering Sciences - Honoring J. Tinsley Oden. 10.1016/j.cma.2009.01.007.
    • (2009) Comput. Methods Appl. Mech. Eng. , vol.198 , Issue.21-26 , pp. 1766-1774
    • Kubatko, E.J.1    Bunya, S.2    Dawson, C.3    Westerink, J.J.4
  • 24
    • 66149136531 scopus 로고    scopus 로고
    • A performance comparison of continuous and discontinuous finite element shallow water models
    • ISSN 0885-7474. URL
    • Kubatko E.J., Bunya S., Dawson C., Westerink J.J., Mirabito C. A performance comparison of continuous and discontinuous finite element shallow water models. J. Sci. Comput. 2009, 40(1-3):315-339. ISSN 0885-7474. URL http://dx.doi.org/10.1007/s10915-009-9268-2. 10.1007/s10915-009-9268-2.
    • (2009) J. Sci. Comput. , vol.40 , Issue.1-3 , pp. 315-339
    • Kubatko, E.J.1    Bunya, S.2    Dawson, C.3    Westerink, J.J.4    Mirabito, C.5
  • 25
    • 76749116655 scopus 로고    scopus 로고
    • A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods
    • ISSN 0377-0427, doi:.2009.05.028
    • Kuzmin D. A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods. J. Comput. Appl. Math. 2010, 233(12):3077-3085. ISSN 0377-0427, doi: http://dx.doi.org/10.1016/j.cam.2009.05.028.
    • (2010) J. Comput. Appl. Math. , vol.233 , Issue.12 , pp. 3077-3085
    • Kuzmin, D.1
  • 26
    • 2442475431 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for nonlinear dispersive equations
    • ISSN 0021-9991
    • Levy D., Shu C.-W., Yan J. Local discontinuous Galerkin methods for nonlinear dispersive equations. J. Comput. Phys. 2004, 196(2):751-772. ISSN 0021-9991.
    • (2004) J. Comput. Phys. , vol.196 , Issue.2 , pp. 751-772
    • Levy, D.1    Shu, C.-W.2    Yan, J.3
  • 27
    • 46749092411 scopus 로고    scopus 로고
    • Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction
    • (electronic) ISSN 0036-1429. URL
    • Liu Y., Shu C.-W., Tadmor E., Zhang M. Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. SIAM J. Numer. Anal. 2007, 45(6):2442-2467. (electronic) ISSN 0036-1429. URL http://dx.doi.org/10.1137/060666974. 10.1137/060666974.
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.6 , pp. 2442-2467
    • Liu, Y.1    Shu, C.-W.2    Tadmor, E.3    Zhang, M.4
  • 28
    • 50249113756 scopus 로고    scopus 로고
    • A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids
    • ISSN 0021-9991. URL
    • Luo H., Baum J., Lhner R. A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids. J. Comput. Phys. 2008, 227(20):8875-8893. ISSN 0021-9991. URL http://www.sciencedirect.com/science/article/B6WHY-4T13CS3-2/2/cacbb700cf043776d94ac1bd3a985bed. 10.1016/j.jcp.2008.06.035.
    • (2008) J. Comput. Phys. , vol.227 , Issue.20 , pp. 8875-8893
    • Luo, H.1    Baum, J.2    Lhner, R.3
  • 29
    • 70349745704 scopus 로고    scopus 로고
    • Quantum hydrodynamics with trajectories: the nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry
    • ISSN 0021-9991. URL.2009.08.011
    • Michoski C., Evans J.A., Schmitz P.G., Vasseur A. Quantum hydrodynamics with trajectories: the nonlinear conservation form mixed/discontinuous Galerkin method with applications in chemistry. J. Comput. Phys. 2009, 228(23):8589-8608. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2009.08.011. 10.1016/j.jcp.2009.08.011.
    • (2009) J. Comput. Phys. , vol.228 , Issue.23 , pp. 8589-8608
    • Michoski, C.1    Evans, J.A.2    Schmitz, P.G.3    Vasseur, A.4
  • 30
    • 85189839993 scopus 로고    scopus 로고
    • Multiscale discontinuous Galerkin hp-adaptive chemical reacters I: quiescent reactors, preprint
    • C. Michoski, J.A. Evans, P.G. Schmitz, Multiscale discontinuous Galerkin hp-adaptive chemical reacters I: quiescent reactors, preprint, 2011a.
    • (2011)
    • Michoski, C.1    Evans, J.A.2    Schmitz, P.G.3
  • 31
    • 73649089238 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for viscous compressible multifluids
    • ISSN 0021-9991. URL.2009.11.033
    • Michoski C., Evans J.A., Schmitz P.G., Vasseur A. A discontinuous Galerkin method for viscous compressible multifluids. J. Comput. Phys. 2010, 229(6):2249-2266. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2009.11.033. 10.1016/j.jcp.2009.11.033.
    • (2010) J. Comput. Phys. , vol.229 , Issue.6 , pp. 2249-2266
    • Michoski, C.1    Evans, J.A.2    Schmitz, P.G.3    Vasseur, A.4
  • 32
    • 67349116002 scopus 로고    scopus 로고
    • Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow
    • ISSN 0021-9991.URL.2009.04.039
    • Murillo J., Garci{dotless}́a-Navarro P., Burguete J. Conservative numerical simulation of multi-component transport in two-dimensional unsteady shallow water flow. J. Comput. Phys. 2009, 228(15):5539-5573. ISSN 0021-9991.URL http://dx.doi.org/10.1016/j.jcp.2009.04.039. 10.1016/j.jcp.2009.04.039.
    • (2009) J. Comput. Phys. , vol.228 , Issue.15 , pp. 5539-5573
    • Murillo, J.1    Garcí a-Navarro, P.2    Burguete, J.3
  • 33
    • 48549103454 scopus 로고    scopus 로고
    • Sub-cell shock capturing and spacetime discontinuity tracking for nonlinear conservation laws
    • ISSN 0271-2091. URL
    • Palaniappan J., Miller S.T., Haber R.B. Sub-cell shock capturing and spacetime discontinuity tracking for nonlinear conservation laws. Int. J. Numer. Methods Fluids 2008, 57(9):1115-1135. ISSN 0271-2091. URL http://dx.doi.org/10.1002/fld.1850. 10.1002/fld.1850.
    • (2008) Int. J. Numer. Methods Fluids , vol.57 , Issue.9 , pp. 1115-1135
    • Palaniappan, J.1    Miller, S.T.2    Haber, R.B.3
  • 34
    • 85189836753 scopus 로고    scopus 로고
    • Sub-cell shock capturing for discontinuous Galerkin methods, Forty-fourth AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA., Online: 5-18
    • P.P. Persson, J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods, Forty-fourth AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA., Online: 5-18, 2006.
    • (2006)
    • Persson, P.P.1    Peraire, J.2
  • 35
    • 19644381369 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin method using WENO limiters
    • Qiu J.X., Shu C.W. Runge-Kutta discontinuous Galerkin method using WENO limiters. Siam J. Sci. Comput. 2005, 26(3):907-929.
    • (2005) Siam J. Sci. Comput. , vol.26 , Issue.3 , pp. 907-929
    • Qiu, J.X.1    Shu, C.W.2
  • 36
    • 32944469214 scopus 로고    scopus 로고
    • Global optimization of explicit strong-stability-preserving Runge-Kutta methods
    • (electronic) ISSN 0025-5718. URL
    • Ruuth S.J. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Math. Comp. 2006, 75(253):183-207. (electronic) ISSN 0025-5718. URL http://dx.doi.org/10.1090/S0025-5718-05-01772-2. 10.1090/S0025-5718-05-01772-2.
    • (2006) Math. Comp. , vol.75 , Issue.253 , pp. 183-207
    • Ruuth, S.J.1
  • 37
    • 45449125925 scopus 로고
    • Efficient implementation of essentially nonoscillatory shock-capturing schemes
    • ISSN 0021-9991
    • Shu C.-W., Osher S. Efficient implementation of essentially nonoscillatory shock-capturing schemes. J. Comput. Phys. 1988, 77(2):439-471. ISSN 0021-9991.
    • (1988) J. Comput. Phys. , vol.77 , Issue.2 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 38
    • 0003423678 scopus 로고
    • Numerical partial differential equations: finite difference methods
    • Springer-Verlag, New York, ISBN 0-387-97999-9
    • Thomas J.W. Numerical partial differential equations: finite difference methods. Texts in Applied Mathematics 1995, vol. 22. Springer-Verlag, New York, ISBN 0-387-97999-9.
    • (1995) Texts in Applied Mathematics , vol.22
    • Thomas, J.W.1
  • 39
    • 44649131248 scopus 로고    scopus 로고
    • Hall magnetohydrodynamics on block-adaptive grids
    • ISSN 0021-9991. URL.2008.04.010
    • Tóth G., Ma Y., Gombosi T.I. Hall magnetohydrodynamics on block-adaptive grids. J. Comput. Phys. 2008, 227(14):6967-6984. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2008.04.010. 10.1016/j.jcp.2008.04.010.
    • (2008) J. Comput. Phys. , vol.227 , Issue.14 , pp. 6967-6984
    • Tóth, G.1    Ma, Y.2    Gombosi, T.I.3
  • 40
    • 0001122872 scopus 로고    scopus 로고
    • Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method [J. Comput. Phys. 32(1) (1979) 101-136]
    • ISSN 0021-9991. With an introduction by Ch. Hirsch, Commemoration of the 30th anniversary {of J. Comput. Phys.}
    • van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method [J. Comput. Phys. 32(1) (1979) 101-136]. J. Comput. Phys. 1997, 135(2):227-248. ISSN 0021-9991. With an introduction by Ch. Hirsch, Commemoration of the 30th anniversary {of J. Comput. Phys.}.
    • (1997) J. Comput. Phys. , vol.135 , Issue.2 , pp. 227-248
    • van Leer, B.1
  • 41
    • 69049085439 scopus 로고    scopus 로고
    • Adjoint-based hp adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
    • ISSN 0021-9991. URL.2009.07.012
    • Wang L., Mavriplis D.J. Adjoint-based hp adaptive discontinuous Galerkin methods for the 2D compressible Euler equations. J. Comput. Phys. 2009, 228(20):7643-7661. ISSN 0021-9991. URL http://dx.doi.org/10.1016/j.jcp.2009.07.012. 10.1016/j.jcp.2009.07.012.
    • (2009) J. Comput. Phys. , vol.228 , Issue.20 , pp. 7643-7661
    • Wang, L.1    Mavriplis, D.J.2
  • 42
    • 78649443328 scopus 로고    scopus 로고
    • A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state
    • ISSN 0021-9991 URL
    • Ward G.M., Pullin D.I. A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state. J. Comput. Phys. 2010, 229(8):2999-3018. ISSN 0021-9991 URL http://dx.doi.org/10.1016/j.jcp.2009.12.027. 10.1016/j.jcp.2009.12.027.
    • (2010) J. Comput. Phys. , vol.229 , Issue.8 , pp. 2999-3018
    • Ward, G.M.1    Pullin, D.I.2
  • 43
    • 59149098014 scopus 로고    scopus 로고
    • Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells
    • (ISSN 0021-9991)
    • Xu Z., Liu Y., Shu C.W. Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells. Comput. Phys. 2009, 228:194-2212. doi: http://dx.doi.org/10.1016/j.jcp.2008.11.025. URL http://dx.doi.org/10.1016/j.jcp.2008.11.025 (ISSN 0021-9991).
    • (2009) Comput. Phys. , vol.228 , pp. 194-2212
    • Xu, Z.1    Liu, Y.2    Shu, C.W.3
  • 44
    • 40849107737 scopus 로고    scopus 로고
    • Runge-kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
    • Zhu J., Qiu J.X., Shu C.W., Dumbser M. Runge-kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes. J. Comput. Phys. 2008, 227(9):4330-4353.
    • (2008) J. Comput. Phys. , vol.227 , Issue.9 , pp. 4330-4353
    • Zhu, J.1    Qiu, J.X.2    Shu, C.W.3    Dumbser, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.