메뉴 건너뛰기




Volumn 59, Issue 12, 2009, Pages 1389-1409

A practical implementation of high-order RKDG models for the 1D open-channel flow equations

Author keywords

1D; Adaptive limiting; High order; RKDG; Saint Venant; Source terms

Indexed keywords

1D; ADAPTIVE LIMITING; HIGH ORDER; RKDG; SAINT VENANT; SOURCE TERMS;

EID: 66149101388     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1879     Document Type: Article
Times cited : (9)

References (60)
  • 7
    • 33846266812 scopus 로고    scopus 로고
    • Upwind and high-resolution methods for compressible flow: From donor cell to residual-distribution schemes
    • van Leer B. Upwind and high-resolution methods for compressible flow: from donor cell to residual-distribution schemes. Communications in Computational Physics 2006; 1(2):192-206.
    • (2006) Communications in Computational Physics , vol.1 , Issue.2 , pp. 192-206
    • van Leer, B.1
  • 8
    • 37449028402 scopus 로고    scopus 로고
    • Godunov-type methods for free-surface shallow flows: A review
    • Toro EF, García-Navarro P. Godunov-type methods for free-surface shallow flows: a review. Journal of Hydraulic Research 2007; 45(6):737-751.
    • (2007) Journal of Hydraulic Research , vol.45 , Issue.6 , pp. 737-751
    • Toro, E.F.1    García-Navarro, P.2
  • 9
    • 0035975580 scopus 로고    scopus 로고
    • Efficient construction of high-resolution TVD conservative schemes for equations with source terms: Application to shallow water flows
    • Burguete J, García-Navarro P. Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows. International Journal for Numerical Methods in Fluids 2001; 37(2):209-248.
    • (2001) International Journal for Numerical Methods in Fluids , vol.37 , Issue.2 , pp. 209-248
    • Burguete, J.1    García-Navarro, P.2
  • 12
    • 7244250223 scopus 로고    scopus 로고
    • Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations
    • Črnjarić-Ž. ic N, Vuković S, Sopta L. Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations. Journal of Computational Physics 2004; 200(2):512-548.
    • (2004) Journal of Computational Physics , vol.200 , Issue.2 , pp. 512-548
    • Črnjarić-Ž1    ic, N.2    Vuković, S.3    Sopta, L.4
  • 16
    • 0003908527 scopus 로고
    • Über die partiellen differenzangleichungen der mathematisches.
    • Courant R, Friedrichs KO, Lewy H. Über die partiellen differenzangleichungen der mathematisches. Mathematische Annalen 1928; 100(1):32-74.
    • (1928) Mathematische Annalen , vol.100 , Issue.1 , pp. 32-74
    • Courant, R.1    Friedrichs, K.O.2    Lewy, H.3
  • 17
    • 33750319371 scopus 로고    scopus 로고
    • A conservative extension of the method of characteristics for 1-D shallow flows
    • Mohammadian A, Le Roux DY, Tajrishi M. A conservative extension of the method of characteristics for 1-D shallow flows. Applied Mathematical Modelling 2007; 31(2):332-348.
    • (2007) Applied Mathematical Modelling , vol.31 , Issue.2 , pp. 332-348
    • Mohammadian, A.1    Le Roux, D.Y.2    Tajrishi, M.3
  • 18
    • 38049095061 scopus 로고    scopus 로고
    • ADER schemes for the shallow water equations in channel with irregular bottom elevation
    • Vignoli G, Titarev VA, Toro EF. ADER schemes for the shallow water equations in channel with irregular bottom elevation. Journal of Computational Physics 2008; 227(4):2463-2480.
    • (2008) Journal of Computational Physics , vol.227 , Issue.4 , pp. 2463-2480
    • Vignoli, G.1    Titarev, V.A.2    Toro, E.F.3
  • 19
    • 29144466580 scopus 로고    scopus 로고
    • Derivative Riemann solvers for systems of conservation laws and ADER Methods
    • Toro EF, Titarev VA. Derivative Riemann solvers for systems of conservation laws and ADER Methods. Journal of Computational Physics 2006; 212(1):150-165.
    • (2006) Journal of Computational Physics , vol.212 , Issue.1 , pp. 150-165
    • Toro, E.F.1    Titarev, V.A.2
  • 20
    • 0000935266 scopus 로고
    • Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov SK. Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics. Matematicheskii Sbornik 1959; 47(3):271-306.
    • (1959) Matematicheskii Sbornik , vol.47 , Issue.3 , pp. 271-306
    • Godunov, S.K.1
  • 21
    • 7544220935 scopus 로고    scopus 로고
    • Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods
    • Zhou T, Li Y, Shu CW. Numerical comparison of WENO finite volume and Runge-Kutta discontinuous Galerkin methods. Journal of Scientific Computing 2001; 16(2):145-171.
    • (2001) Journal of Scientific Computing , vol.16 , Issue.2 , pp. 145-171
    • Zhou, T.1    Li, Y.2    Shu, C.W.3
  • 22
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equations and their numerical computation
    • Lax PD. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Communications of Pure and Applied Mathematics 1954; 7(1):159-193.
    • (1954) Communications of Pure and Applied Mathematics , vol.7 , Issue.1 , pp. 159-193
    • Lax, P.D.1
  • 23
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics 1983; 49(3):357-393.
    • (1983) Journal of Computational Physics , vol.49 , Issue.3 , pp. 357-393
    • Harten, A.1
  • 24
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
    • Kurganov A, Tadmor E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. Journal of Computational Physics 2000; 160(1):241-282.
    • (2000) Journal of Computational Physics , vol.160 , Issue.1 , pp. 241-282
    • Kurganov, A.1    Tadmor, E.2
  • 25
    • 33749583060 scopus 로고
    • Flux corrected transport I, SHASTA, a fluid transport algorithm that works
    • Boris JP, Book DL. Flux corrected transport I, SHASTA, a fluid transport algorithm that works. Journal of Computational Physics 1973; 11(1):38-69.
    • (1973) Journal of Computational Physics , vol.11 , Issue.1 , pp. 38-69
    • Boris, J.P.1    Book, D.L.2
  • 26
    • 34547419627 scopus 로고
    • The piecewise parabolic method (PPM) for gas-dynamical simulation
    • Colella P, Woodward P. The piecewise parabolic method (PPM) for gas-dynamical simulation. Journal of Computational Physics 1984; 54(1):174-201.
    • (1984) Journal of Computational Physics , vol.54 , Issue.1 , pp. 174-201
    • Colella, P.1    Woodward, P.2
  • 28
    • 0023329384 scopus 로고
    • Uniformly high-order accurate nonoscillatory schemes I
    • Harten A, Osher S. Uniformly high-order accurate nonoscillatory schemes I. SIAM Journal on Numerical Analysis 1987; 24(2):279-309.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , Issue.2 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 30
    • 0022144821 scopus 로고
    • Convergence of generalized MUSCL schemes
    • Osher S. Convergence of generalized MUSCL schemes. SIAM Journal on Numerical Analysis 1984; 22(5):947-961.
    • (1984) SIAM Journal on Numerical Analysis , vol.22 , Issue.5 , pp. 947-961
    • Osher, S.1
  • 31
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock capturing schemes. Journal of Computational Physics 1988; 77(2):439-471.
    • (1988) Journal of Computational Physics , vol.77 , Issue.2 , pp. 439-471
    • Shu, C.W.1    Osher, S.2
  • 32
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • Sweby PK. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis 1984; 21(5):995-1011.
    • (1984) SIAM Journal on Numerical Analysis , vol.21 , Issue.5 , pp. 995-1011
    • Sweby, P.K.1
  • 33
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme
    • van Leer B. Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme. Journal of Computational Physics 1974; 14(4):361-370.
    • (1974) Journal of Computational Physics , vol.14 , Issue.4 , pp. 361-370
    • van Leer, B.1
  • 34
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin method for convection-dominated problems
    • Cockburn B, Shu CW. Runge-Kutta discontinuous Galerkin method for convection-dominated problems. Journal of Scientific Computing 2001; 16(3):173-261.
    • (2001) Journal of Scientific Computing , vol.16 , Issue.3 , pp. 173-261
    • Cockburn, B.1    Shu, C.W.2
  • 36
    • 38349119964 scopus 로고    scopus 로고
    • Riemann solvers with Runge-Kutta discontinuous Galerkin schemes for the 1D shallow water equations
    • Kesserwani G, Ghostine R, Vazquez J, Ghenaim A, Mosé R. Riemann solvers with Runge-Kutta discontinuous Galerkin schemes for the 1D shallow water equations. Journal of Hydraulic Engineering 2008; 134(2):243-255.
    • (2008) Journal of Hydraulic Engineering , vol.134 , Issue.2 , pp. 243-255
    • Kesserwani, G.1    Ghostine, R.2    Vazquez, J.3    Ghenaim, A.4    Mosé, R.5
  • 37
    • 0001695533 scopus 로고
    • Efficient construction and utilization of approximate Riemann solutions
    • Glowinski R, Lions JL eds, North-Holland: Amsterdam
    • Roe PL, Pike J. Efficient construction and utilization of approximate Riemann solutions. In Proceedings of Computing Methods in Applied Science and Engineering, Glowinski R, Lions JL (eds). North-Holland: Amsterdam, 1984.
    • (1984) Proceedings of Computing Methods in Applied Science and Engineering
    • Roe, P.L.1    Pike, J.2
  • 38
    • 0002203252 scopus 로고
    • Riemann problems and the WAF method for solving the two dimensional shallow water equations
    • Toro EF. Riemann problems and the WAF method for solving the two dimensional shallow water equations. Philosophical Transactions of the Royal Society of London 1992; 338(1649):43-68.
    • (1992) Philosophical Transactions of the Royal Society of London , vol.338 , Issue.1649 , pp. 43-68
    • Toro, E.F.1
  • 39
    • 0028407037 scopus 로고
    • Parallel, adaptive finite element methods for conservation laws
    • Biswas R, Devine KD, Flaherty J. Parallel, adaptive finite element methods for conservation laws. Applied Numerical Mathematics 1994; 14(1-3):255-283.
    • (1994) Applied Numerical Mathematics , vol.14 , Issue.1-3 , pp. 255-283
    • Biswas, R.1    Devine, K.D.2    Flaherty, J.3
  • 40
    • 34548444530 scopus 로고    scopus 로고
    • Limiters for high-order discontinuous Galerkin methods
    • Krivodonova L. Limiters for high-order discontinuous Galerkin methods. Journal of Computational Physics 2007; 226(1):276-296.
    • (2007) Journal of Computational Physics , vol.226 , Issue.1 , pp. 276-296
    • Krivodonova, L.1
  • 41
    • 11144343214 scopus 로고    scopus 로고
    • An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods
    • Zhang M, Shu CW. An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Computers and Fluids 2005; 34(4-5):581-592.
    • (2005) Computers and Fluids , vol.34 , Issue.4-5 , pp. 581-592
    • Zhang, M.1    Shu, C.W.2
  • 42
    • 0003630916 scopus 로고
    • Triangular mesh methods for the neutron transport equation
    • Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM
    • Reed W, Hill T. Triangular mesh methods for the neutron transport equation. Technical Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM, 1973.
    • (1973)
    • Reed, W.1    Hill, T.2
  • 43
    • 2142822267 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for the shallow water equations with source terms
    • Discontinuous Galerkin Methods, Cockburn B, Karniadakis G, Shu CW eds, Springer: Berlin
    • Schwanenberg D, Kongeter J. A discontinuous Galerkin method for the shallow water equations with source terms. In Discontinuous Galerkin Methods, Cockburn B, Karniadakis G, Shu CW (eds). Lecture Notes in Computational Science and Engineering, vol. 11. Springer: Berlin, 2000; 419-424.
    • (2000) Lecture Notes in Computational Science and Engineering , vol.11 , pp. 419-424
    • Schwanenberg, D.1    Kongeter, J.2
  • 45
    • 46749092411 scopus 로고    scopus 로고
    • Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction
    • Liu Y, Shu C-W, Tadmor E, Zhang M. Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. SIAM Journal on Numerical Analysis 2007; 45(6):2442-2467.
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.6 , pp. 2442-2467
    • Liu, Y.1    Shu, C.-W.2    Tadmor, E.3    Zhang, M.4
  • 46
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • Nessyahu H, Tadmor E. Non-oscillatory central differencing for hyperbolic conservation laws. Journal of Computational Physics 1990; 87(2):408-463.
    • (1990) Journal of Computational Physics , vol.87 , Issue.2 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 47
    • 33745038766 scopus 로고    scopus 로고
    • Building blocks for arbitrary high order discontinuous Galerkin schemes
    • Dumbser M, Munz CD. Building blocks for arbitrary high order discontinuous Galerkin schemes. Journal of Scientific Computing 2006; 27(1-3):215-230.
    • (2006) Journal of Scientific Computing , vol.27 , Issue.1-3 , pp. 215-230
    • Dumbser, M.1    Munz, C.D.2
  • 48
    • 27144507034 scopus 로고    scopus 로고
    • ADER discontinuous Galerkin for aeroacoustics
    • Dumbser M, Munz CD. ADER discontinuous Galerkin for aeroacoustics. Comptes Rendus Mécanique 2005; 333(9):683-687.
    • (2005) Comptes Rendus Mécanique , vol.333 , Issue.9 , pp. 683-687
    • Dumbser, M.1    Munz, C.D.2
  • 50
    • 33644933296 scopus 로고    scopus 로고
    • High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
    • Xing Y, Shu CW. High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Journal of Computational Physics 2006; 14(2):567-598.
    • (2006) Journal of Computational Physics , vol.14 , Issue.2 , pp. 567-598
    • Xing, Y.1    Shu, C.W.2
  • 51
    • 17444431952 scopus 로고    scopus 로고
    • Flooding and drying in discontinuous Galerkin finite-element discretizations of shallow-water equations. Part I: One dimension
    • Bokhove O. Flooding and drying in discontinuous Galerkin finite-element discretizations of shallow-water equations. Part I: one dimension. Journal of Scientific Computing 2005; 22-23:47-82.
    • (2005) Journal of Scientific Computing , vol.22-23 , pp. 47-82
    • Bokhove, O.1
  • 52
    • 34247217171 scopus 로고    scopus 로고
    • Space-time discontinuous Galerkin finite element method for shallow water flows
    • Ambati VR, Bokhove O. Space-time discontinuous Galerkin finite element method for shallow water flows. Journal of Computational and Applied Mathematics 2006; 204(2):452-462.
    • (2006) Journal of Computational and Applied Mathematics , vol.204 , Issue.2 , pp. 452-462
    • Ambati, V.R.1    Bokhove, O.2
  • 53
    • 50249160362 scopus 로고    scopus 로고
    • A new wetting and drying algorithm for discontinuous Galerkin solutions to the shallow water equations
    • Los Angeles, U.S.A
    • Bunya S, Westerink J, Kubatko E, Dawson C. A new wetting and drying algorithm for discontinuous Galerkin solutions to the shallow water equations. World Congress on Computational Mechanics, vol. 7, Los Angeles, U.S.A., 2006.
    • (2006) World Congress on Computational Mechanics , vol.7
    • Bunya, S.1    Westerink, J.2    Kubatko, E.3    Dawson, C.4
  • 54
    • 50249144099 scopus 로고
    • A well-balanced Runge-Kutta Discontinuous Galerkin method for the shallowwater equations with flooding and drying
    • DOI: 10.1002/fld
    • Ern A, Piperno S, Djadel K. A well-balanced Runge-Kutta Discontinuous Galerkin method for the shallowwater equations with flooding and drying. International Journal for Numerical Methods in Fluids 2008; DOI: 10.1002/fld.1674.
    • (1674) International Journal for Numerical Methods in Fluids , vol.2008
    • Ern, A.1    Piperno, S.2    Djadel, K.3
  • 58
    • 33745457668 scopus 로고    scopus 로고
    • Numerical boundary conditions for globally mass conservative methods to solve the shallow water equations and applied to river flow
    • Burguete J, Garc'ia-Navarro P, Murillo J. Numerical boundary conditions for globally mass conservative methods to solve the shallow water equations and applied to river flow. International Journal for Numerical Methods in Fluids 2006; 51(6):585-675.
    • (2006) International Journal for Numerical Methods in Fluids , vol.51 , Issue.6 , pp. 585-675
    • Burguete, J.1    Garc'ia-Navarro, P.2    Murillo, J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.