-
1
-
-
0035399783
-
Exact solutions to the Riemann problem of the shallow water equations with a bottom step
-
Alcrudo F., and Benkhaldoun F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Comput. Fluids 30 (2001) 643-671
-
(2001)
Comput. Fluids
, vol.30
, pp. 643-671
-
-
Alcrudo, F.1
Benkhaldoun, F.2
-
2
-
-
4644342716
-
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
-
Audusse E., Bouchut F., Bristeau M.-O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp. 25 (2004) 2050-2065
-
(2004)
SIAM J. Sci. Comp.
, vol.25
, pp. 2050-2065
-
-
Audusse, E.1
Bouchut, F.2
Bristeau, M.-O.3
Klein, R.4
Perthame, B.5
-
3
-
-
0028534347
-
Upwind methods for hyperbolic conservation laws with source terms
-
Bernudez A., and Vazquez M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 1049-1071
-
(1994)
Comput. Fluids
, vol.23
, pp. 1049-1071
-
-
Bernudez, A.1
Vazquez, M.E.2
-
4
-
-
0037234915
-
Equilibrium schemes for scalar conservation laws with stiff sources
-
Botchorishvili R., Perthame B., and Vasseur A. Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comp. 72 241 (2003) 131-157
-
(2003)
Math. Comp.
, vol.72
, Issue.241
, pp. 131-157
-
-
Botchorishvili, R.1
Perthame, B.2
Vasseur, A.3
-
5
-
-
85190102839
-
-
A. Chinnayya, A.Y. Le Roux, A new general Riemann solver for the shallow-water equations with friction and topography, 1999, preprint.
-
-
-
-
6
-
-
85190144140
-
-
A. Chinnayya, A.Y. Le Roux, N. Seguin, A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon, 2003, preprint.
-
-
-
-
7
-
-
0037280087
-
Improved application of the HLLE Riemann solver for the shallow water equations with source terms
-
Delis A.I. Improved application of the HLLE Riemann solver for the shallow water equations with source terms. Commun. Numer. Meth. Eng. 19 (2003) 59-83
-
(2003)
Commun. Numer. Meth. Eng.
, vol.19
, pp. 59-83
-
-
Delis, A.I.1
-
8
-
-
0037429776
-
Relaxation schemes for the shallow water equations
-
Delis A.I., and Katsaounis Th. Relaxation schemes for the shallow water equations. Int. J. Numer. Meth. Fluids 41 (2003) 695-719
-
(2003)
Int. J. Numer. Meth. Fluids
, vol.41
, pp. 695-719
-
-
Delis, A.I.1
Katsaounis, Th.2
-
10
-
-
0037404907
-
Some approximate Godunov schemes to compute shallow-water equations with topography
-
Gallouët T., Hérard J.-M., and Seguin N. Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479-513
-
(2003)
Comput. Fluids
, vol.32
, pp. 479-513
-
-
Gallouët, T.1
Hérard, J.-M.2
Seguin, N.3
-
11
-
-
0001400845
-
The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow
-
Glaz H.M., and Liu T.P. The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow. Adv. Appl. Math. 5 (1984) 111-146
-
(1984)
Adv. Appl. Math.
, vol.5
, pp. 111-146
-
-
Glaz, H.M.1
Liu, T.P.2
-
12
-
-
0000935266
-
Finite difference schemes for numerical computation of solutions of the equations of fluid dynamics
-
Godunov S.K. Finite difference schemes for numerical computation of solutions of the equations of fluid dynamics. Math. USSR Sbornik 47 (1959) 271-306
-
(1959)
Math. USSR Sbornik
, vol.47
, pp. 271-306
-
-
Godunov, S.K.1
-
13
-
-
0034209981
-
A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
-
Gosse L. A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. Appl. 39 (2000) 135-159
-
(2000)
Comput. Math. Appl.
, vol.39
, pp. 135-159
-
-
Gosse, L.1
-
14
-
-
0035590547
-
A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms
-
Gosse L. A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math. Models Methods Appl. Sci. 11 2 (2001) 339-365
-
(2001)
Math. Models Methods Appl. Sci.
, vol.11
, Issue.2
, pp. 339-365
-
-
Gosse, L.1
-
15
-
-
0000711631
-
A well-balanced scheme designed for inhomogeneous scalar conservation laws
-
Gosse L., and Le Roux A.-Y. A well-balanced scheme designed for inhomogeneous scalar conservation laws. C. R. Acad. Sci., Paris. Sér I 323 (1996) 543-546
-
(1996)
C. R. Acad. Sci., Paris. Sér I
, vol.323
, pp. 543-546
-
-
Gosse, L.1
Le Roux, A.-Y.2
-
16
-
-
1542576141
-
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
-
Greenberg J.M., and Le Roux A.-Y. A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1-16
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 1-16
-
-
Greenberg, J.M.1
Le Roux, A.-Y.2
-
18
-
-
0000876320
-
On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
-
Harten A., Lax P.D., and Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1983) 35-61
-
(1983)
SIAM Rev.
, vol.25
, pp. 35-61
-
-
Harten, A.1
Lax, P.D.2
Van Leer, B.3
-
19
-
-
0011032642
-
Flux difference splitting and the balancing of source terms and flux gradients
-
Hubbard M.E., and Garcia-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165 (2000) 89-125
-
(2000)
J. Comput. Phys.
, vol.165
, pp. 89-125
-
-
Hubbard, M.E.1
Garcia-Navarro, P.2
-
20
-
-
28144455569
-
Non-oscillatory central differencing for hyperbolic conservation laws
-
Nessyahu H., and Tadmor E. Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463
-
(1990)
J. Comput. Phys.
, vol.87
, pp. 408-463
-
-
Nessyahu, H.1
Tadmor, E.2
-
21
-
-
0035537697
-
A steady-state capturing method for hyperbolic system with geometrical source terms
-
Jin S. A steady-state capturing method for hyperbolic system with geometrical source terms. Math. Model. Numer. Anal. 35 (2001) 631-646
-
(2001)
Math. Model. Numer. Anal.
, vol.35
, pp. 631-646
-
-
Jin, S.1
-
22
-
-
0030188150
-
The effects of numerical viscosities I. Slowly moving shocks
-
Jin S., and Liu J.-G. The effects of numerical viscosities I. Slowly moving shocks. J. Comput. Phys. 126 (1996) 373-389
-
(1996)
J. Comput. Phys.
, vol.126
, pp. 373-389
-
-
Jin, S.1
Liu, J.-G.2
-
23
-
-
3042753342
-
An efficient method for computing hyperbolic systems with geometrical source terms having concentrations
-
Jin S., and Wen X. An efficient method for computing hyperbolic systems with geometrical source terms having concentrations. J. Comput. Math. 22 (2004) 230-249
-
(2004)
J. Comput. Math.
, vol.22
, pp. 230-249
-
-
Jin, S.1
Wen, X.2
-
24
-
-
27844586617
-
Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations
-
Jin S., and Wen X. Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations. SIAM J. Sci. Comp. 26 (2005) 2079-2101
-
(2005)
SIAM J. Sci. Comp.
, vol.26
, pp. 2079-2101
-
-
Jin, S.1
Wen, X.2
-
25
-
-
84990701264
-
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
-
Jin S., and Xin Z.-P. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Commun. Pure Appl. Math. XLVIII (1995) 235-276
-
(1995)
Commun. Pure Appl. Math.
, vol.XLVIII
, pp. 235-276
-
-
Jin, S.1
Xin, Z.-P.2
-
26
-
-
0036333838
-
Central-upwind schemes for the Saint-Venant system
-
Kurganov A., and Levy D. Central-upwind schemes for the Saint-Venant system. Math. Model. Numer. Anal. 36 3 (2002) 397-425
-
(2002)
Math. Model. Numer. Anal.
, vol.36
, Issue.3
, pp. 397-425
-
-
Kurganov, A.1
Levy, D.2
-
27
-
-
0036288577
-
Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
-
Kurganov A., Noelle S., and Petrova G. Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23 3 (2001) 707-740
-
(2001)
SIAM J. Sci. Comput.
, vol.23
, Issue.3
, pp. 707-740
-
-
Kurganov, A.1
Noelle, S.2
Petrova, G.3
-
28
-
-
5744243501
-
The riemann problem for fluid flows in a nozzle with discontinuous cross-section
-
LeFloch P.G., and Thanh M.D. The riemann problem for fluid flows in a nozzle with discontinuous cross-section. Commun. Math. Sci. 1 (2003) 763-797
-
(2003)
Commun. Math. Sci.
, vol.1
, pp. 763-797
-
-
LeFloch, P.G.1
Thanh, M.D.2
-
30
-
-
0001315315
-
Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm
-
LeVeque R.J. Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346-365
-
(1998)
J. Comput. Phys.
, vol.146
, pp. 346-365
-
-
LeVeque, R.J.1
-
31
-
-
0012588539
-
A kinetic scheme for the Saint-Venant system with a source term
-
Perthame B., and Simeoni C. A kinetic scheme for the Saint-Venant system with a source term. CALCOLO 38 4 (2001) 201-231
-
(2001)
CALCOLO
, vol.38
, Issue.4
, pp. 201-231
-
-
Perthame, B.1
Simeoni, C.2
-
32
-
-
85190158413
-
-
Ch. Makridakis, Th. Katsaounis, Relaxation models and finite element schemes for the shallow water equations, in: Thomas Y. Hou, Eitan Tadmor (Eds.), Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002.
-
-
-
-
33
-
-
2942757053
-
Approximate Riemann solvers, parameter vectors, and difference schemes
-
Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357-372
-
(1981)
J. Comput. Phys.
, vol.43
, pp. 357-372
-
-
Roe, P.L.1
-
34
-
-
0003092662
-
Upwinding differenced schemes for hyperbolic conservation laws with source terms
-
Nonlinear Hyperbolic Problems, Proc. Adv. Res. Workshop, St. Étienne, 1986, Springer, Berlin
-
Roe P.L. Upwinding differenced schemes for hyperbolic conservation laws with source terms. Nonlinear Hyperbolic Problems, Proc. Adv. Res. Workshop, St. Étienne, 1986. Lect. Notes Math. vol. 1270 (1987), Springer, Berlin 41-45
-
(1987)
Lect. Notes Math.
, vol.1270
, pp. 41-45
-
-
Roe, P.L.1
-
35
-
-
45449125925
-
Efficient implementation of essentially non-oscillatory shock capturing scheme
-
Shu C.W., and Osher S. Efficient implementation of essentially non-oscillatory shock capturing scheme. J. Comput. Phys. 77 (1988) 439-471
-
(1988)
J. Comput. Phys.
, vol.77
, pp. 439-471
-
-
Shu, C.W.1
Osher, S.2
-
36
-
-
0348194970
-
Improved treatment of source terms in upwind schemes for shallow water equations in channels with irregular geometry
-
Vazquez-Cendon M.E. Improved treatment of source terms in upwind schemes for shallow water equations in channels with irregular geometry. J. Comput. Phys. 148 (1999) 497-526
-
(1999)
J. Comput. Phys.
, vol.148
, pp. 497-526
-
-
Vazquez-Cendon, M.E.1
-
37
-
-
0346736680
-
A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems
-
Wang J.W., and Liu R.X. A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems. Math. Comput. Simul. 53 (2000) 171-184
-
(2000)
Math. Comput. Simul.
, vol.53
, pp. 171-184
-
-
Wang, J.W.1
Liu, R.X.2
-
38
-
-
0037141036
-
A well-balanced gas-kinetic scheme for the shallow water equations with source terms
-
Xu K. A well-balanced gas-kinetic scheme for the shallow water equations with source terms. J. Comput. Phys. 178 2 (2002) 533-562
-
(2002)
J. Comput. Phys.
, vol.178
, Issue.2
, pp. 533-562
-
-
Xu, K.1
-
39
-
-
0037139448
-
Numerical solutions of the shallow water equations with discontinuous bed topography
-
Zhou J.G., Causon D.M., Ingram D.M., and Mingham C.G. Numerical solutions of the shallow water equations with discontinuous bed topography. Int. J. Numer. Meth. Fluids 38 (2002) 769-788
-
(2002)
Int. J. Numer. Meth. Fluids
, vol.38
, pp. 769-788
-
-
Zhou, J.G.1
Causon, D.M.2
Ingram, D.M.3
Mingham, C.G.4
-
40
-
-
0002690008
-
The surface gradient method for the treatment of source terms in the shallow water equations
-
Zhou J.G., Causon D.M., Mingham C.G., and Ingram D.M. The surface gradient method for the treatment of source terms in the shallow water equations. J. Comput. Phys. 168 (2001) 1-25
-
(2001)
J. Comput. Phys.
, vol.168
, pp. 1-25
-
-
Zhou, J.G.1
Causon, D.M.2
Mingham, C.G.3
Ingram, D.M.4
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