-
1
-
-
61849162511
-
Two-layer shallow water systems: A relaxation approach
-
to appear
-
R. ABGRALL AND S. KARNI, Two-layer shallow water systems: A relaxation approach, SIAM J. Sci. Comput., to appear.
-
SIAM J. Sci. Comput
-
-
ABGRALL, R.1
KARNI, S.2
-
2
-
-
18144362100
-
A multilayer Saint-Venant model: Derivation and numerical validation
-
E. AUDUSSE, A multilayer Saint-Venant model: Derivation and numerical validation, Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), pp. 189-214.
-
(2005)
Discrete Contin. Dyn. Syst. Ser. B
, vol.5
, pp. 189-214
-
-
AUDUSSE, E.1
-
3
-
-
0007220703
-
Numerical solutions of one-pressure models in multifluid flows
-
F. BERGER AND J.-F. COLOMBEAU, Numerical solutions of one-pressure models in multifluid flows, SIAM J. Numer. Anal., 32 (1995), pp. 1139-1154.
-
(1995)
SIAM J. Numer. Anal
, vol.32
, pp. 1139-1154
-
-
BERGER, F.1
COLOMBEAU, J.-F.2
-
4
-
-
46749124404
-
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
-
F. BOUCHUT AND T. MORALES DE LUNA, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 683-698.
-
(2008)
M2AN Math. Model. Numer. Anal
, vol.42
, pp. 683-698
-
-
BOUCHUT, F.1
MORALES DE LUNA, T.2
-
5
-
-
0035631410
-
A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
-
M. CASTRO, J. MACÍAS, AND C. PARÉS, A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system, M2AN Math. Model. Numer. Anal., 35 (2001), pp. 107-127.
-
(2001)
M2AN Math. Model. Numer. Anal
, vol.35
, pp. 107-127
-
-
CASTRO, M.1
MACÍAS, J.2
PARÉS, C.3
-
6
-
-
0344286921
-
A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions. Application to the Strait of Gibraltar
-
M.J. CASTRO, J. MACÍAS, C. PARÉ S, J.A. GARCÍA-RODRÍGUEZ, AND E. VÁZQUEZ-CENDÓN, A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions. Application to the Strait of Gibraltar, Commun. Nonlinear Sci. Numer. Simul., 9 (2004), pp. 241-249.
-
(2004)
Commun. Nonlinear Sci. Numer. Simul
, vol.9
, pp. 241-249
-
-
CASTRO, M.J.1
MACÍAS, J.2
PARÉ S, C.3
GARCÍA-RODRÍGUEZ, J.A.4
VÁZQUEZ-CENDÓN, E.5
-
7
-
-
33748787198
-
Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations
-
J.-J. CAURET, J.-F. COLOMBEAU, AND A.Y. LEROUX, Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations, J. Math. Anal. Appl., 139 (1989), pp. 552-573.
-
(1989)
J. Math. Anal. Appl
, vol.139
, pp. 552-573
-
-
CAURET, J.-J.1
COLOMBEAU, J.-F.2
LEROUX, A.Y.3
-
8
-
-
0037636923
-
Generalized solutions to partial differential equations of evolution type
-
J.F. COLOMBEAU, A. HEIBIG, AND M. OBERGUGGENBERGER, Generalized solutions to partial differential equations of evolution type, Acta Appl. Math., 45 (1996), pp. 115-142.
-
(1996)
Acta Appl. Math
, vol.45
, pp. 115-142
-
-
COLOMBEAU, J.F.1
HEIBIG, A.2
OBERGUGGENBERGER, M.3
-
9
-
-
0003245386
-
Multiplication of Distributions: A Tool in Mathematics, Numerical Engineering and Theoretical Physics
-
Springer-Verlag, Berlin
-
J.-F. COLOMBEAU, Multiplication of Distributions: A Tool in Mathematics, Numerical Engineering and Theoretical Physics, Lecture Notes in Math. 1532, Springer-Verlag, Berlin, 1992.
-
(1992)
Lecture Notes in Math
, vol.1532
-
-
COLOMBEAU, J.-F.1
-
10
-
-
0001522672
-
Definition and weak stability of nonconservative products
-
G. DAL MASO, P. G. LEFLOCH, AND F. MURAT, Definition and weak stability of nonconservative products, J. Math. Pures Appl., 74 (1995), pp. 483-548.
-
(1995)
J. Math. Pures Appl
, vol.74
, pp. 483-548
-
-
DAL MASO, G.1
LEFLOCH, P.G.2
MURAT, F.3
-
11
-
-
84868906191
-
-
A.J.C. DE SAINT-VENANT, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivière at à l'introduction des marèes dans leur lit., C.R. Acad. Sci. Paris, 73 (1871), pp. 147-154.
-
A.J.C. DE SAINT-VENANT, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivière at à l'introduction des marèes dans leur lit., C.R. Acad. Sci. Paris, 73 (1871), pp. 147-154.
-
-
-
-
12
-
-
37249012023
-
On wellbalanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems
-
M.J. CASTRO DÍAZ, T. CHACÓN REBOLLO, E.D. FERNÁNDEZ-NIETO, AND C. PARÉS, On wellbalanced finite volume methods for nonconservative nonhomogeneous hyperbolic systems, SIAM J. Sci. Comput., 29 (2007), pp. 1093-1126.
-
(2007)
SIAM J. Sci. Comput
, vol.29
, pp. 1093-1126
-
-
CASTRO DÍAZ, M.J.1
CHACÓN REBOLLO, T.2
FERNÁNDEZ-NIETO, E.D.3
PARÉS, C.4
-
13
-
-
0001394094
-
On Godunov-type methods for gas dynamics
-
B. EINFELDT, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25 (1988), pp. 294-318.
-
(1988)
SIAM J. Numer. Anal
, vol.25
, pp. 294-318
-
-
EINFELDT, B.1
-
14
-
-
0022680530
-
Maximal two-layer exchange over a sill and through a combination of a sill and contraction with barotropic flow
-
D. FARMER AND L. ARMI, Maximal two-layer exchange over a sill and through a combination of a sill and contraction with barotropic flow, J. Fluid Mech., 164 (1986), pp. 53-76.
-
(1986)
J. Fluid Mech
, vol.164
, pp. 53-76
-
-
FARMER, D.1
ARMI, L.2
-
16
-
-
0035273564
-
Strong stability-preserving high-order time discretization methods
-
S. GOTTLIEB, C.-W. SHU, AND E. TADMOR, Strong stability-preserving high-order time discretization methods, SIAM Rev., 43 (2001), pp. 89-112.
-
(2001)
SIAM Rev
, vol.43
, pp. 89-112
-
-
GOTTLIEB, S.1
SHU, C.-W.2
TADMOR, E.3
-
17
-
-
0000876320
-
On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
-
A. HARTEN, P. D. LAX, AND B. VAN LEER, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25 (1983), pp. 35-61.
-
(1983)
SIAM Rev
, vol.25
, pp. 35-61
-
-
HARTEN, A.1
LAX, P.D.2
VAN LEER, B.3
-
18
-
-
84868893541
-
-
D. KRÖNER, Numerical Schemes for Conservation Laws, Adv. Numer. Math., John Wiley & Sons, Chichester, 1997.
-
D. KRÖNER, Numerical Schemes for Conservation Laws, Adv. Numer. Math., John Wiley & Sons, Chichester, 1997.
-
-
-
-
19
-
-
0036333838
-
Central-upwind schemes for the Saint-Venant system
-
A. KURGANOV AND D. LEVY, Central-upwind schemes for the Saint-Venant system, M2AN Math. Model. Numer. Anal., 36 (2002), pp. 397-425.
-
(2002)
M2AN Math. Model. Numer. Anal
, vol.36
, pp. 397-425
-
-
KURGANOV, A.1
LEVY, D.2
-
20
-
-
33846322082
-
On the reduction of numerical dissipation in central-upwind schemes
-
A. KURGANOV AND C.-T. LIN, On the reduction of numerical dissipation in central-upwind schemes, Commun. Comput. Phys., 2 (2007), pp. 141-163.
-
(2007)
Commun. Comput. Phys
, vol.2
, pp. 141-163
-
-
KURGANOV, A.1
LIN, C.-T.2
-
21
-
-
0036288577
-
Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
-
A. KURGANOV, S. NOELLE, AND G. PETROVA, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput., 23 (2001), pp. 707-740.
-
(2001)
SIAM J. Sci. Comput
, vol.23
, pp. 707-740
-
-
KURGANOV, A.1
NOELLE, S.2
PETROVA, G.3
-
22
-
-
34248326790
-
A second-order well-balanced positivity preserving centralupwind scheme for the Saint-Venant system
-
A. KURGANOV AND G. PETROVA, A second-order well-balanced positivity preserving centralupwind scheme for the Saint-Venant system, Commun. Math. Sci., 5 (2007), pp. 133-160.
-
(2007)
Commun. Math. Sci
, vol.5
, pp. 133-160
-
-
KURGANOV, A.1
PETROVA, G.2
-
23
-
-
0347987814
-
New high resolution central schemes for nonlinear conservation laws and convection-diffusion equations
-
A. KURGANOV AND E. TADMOR, New high resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), pp. 241-282.
-
(2000)
J. Comput. Phys
, vol.160
, pp. 241-282
-
-
KURGANOV, A.1
TADMOR, E.2
-
24
-
-
0036735663
-
Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
-
A. KURGANOV AND E. TADMOR, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Methods Partial Differential Equations, 18 (2002), pp. 584-608.
-
(2002)
Numer. Methods Partial Differential Equations
, vol.18
, pp. 584-608
-
-
KURGANOV, A.1
TADMOR, E.2
-
25
-
-
21344434180
-
Graph solutions of nonlinear hyperbolic systems
-
P.G. LEFLOCH, Graph solutions of nonlinear hyperbolic systems, J. Hyperbolic Differ. Equ., 1 (2004), pp. 643-689.
-
(2004)
J. Hyperbolic Differ. Equ
, vol.1
, pp. 643-689
-
-
LEFLOCH, P.G.1
-
27
-
-
0041428206
-
On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws
-
K.-A. LIE AND S. NOELLE, On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws, SIAM J. Sci. Comput., 24 (2003), pp. 1157-1174.
-
(2003)
SIAM J. Sci. Comput
, vol.24
, pp. 1157-1174
-
-
LIE, K.-A.1
NOELLE, S.2
-
28
-
-
0033571987
-
Improvement and generalization of a finite element shallow-water solver to multi-layer systems
-
J. MACÍAS, C. PARES, AND M.J. CASTRO, Improvement and generalization of a finite element shallow-water solver to multi-layer systems, Internat. J. Numer. Methods Fluids, 31 (1999), pp. 1037-1059.
-
(1999)
Internat. J. Numer. Methods Fluids
, vol.31
, pp. 1037-1059
-
-
MACÍAS, J.1
PARES, C.2
CASTRO, M.J.3
-
29
-
-
84868900117
-
On an Estimation of Polynomial Roots by Lagrange
-
Technical report 025/, IRMA, Strasbourg, also available online from
-
M. MIGNOTTE AND D. STEFANESCU, On an Estimation of Polynomial Roots by Lagrange, Technical report 025/2002, IRMA, Strasbourg, 2002; also available online from http://hal.archives-ouvertes.fr/hal-00129675/ en/.
-
(2002)
, pp. 2002
-
-
MIGNOTTE, M.1
STEFANESCU, D.2
-
30
-
-
28144455569
-
Nonoscillatory central differencing for hyperbolic conservation laws
-
H. NESSYAHU AND E. TADMOR, Nonoscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
-
(1990)
J. Comput. Phys
, vol.87
, pp. 408-463
-
-
NESSYAHU, H.1
TADMOR, E.2
-
31
-
-
10044294949
-
On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems
-
C. PARÉS AND M. CASTRO, On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems, M2AN Math. Model. Numer. Anal., 38 (2004), pp. 821-852.
-
(2004)
M2AN Math. Model. Numer. Anal
, vol.38
, pp. 821-852
-
-
PARÉS, C.1
CASTRO, M.2
-
32
-
-
0002699123
-
Theoretical considerations on the motion of salt and fresh water
-
Minneapolis, MN, American Society of Civil Engineers
-
J.B. SCHUF AND J.C. SCHONFELD, Theoretical considerations on the motion of salt and fresh water, in Proceedings of the Minnesota International Hydraulics Conv., Minneapolis, MN, American Society of Civil Engineers, 1953, pp. 321-333.
-
(1953)
Proceedings of the Minnesota International Hydraulics Conv
, pp. 321-333
-
-
SCHUF, J.B.1
SCHONFELD, J.C.2
-
33
-
-
0000564951
-
Total-variation-diminishing time discretizations
-
C.-W. SHU, Total-variation-diminishing time discretizations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 1073-1084.
-
(1988)
SIAM J. Sci. Stat. Comput
, vol.9
, pp. 1073-1084
-
-
SHU, C.-W.1
-
34
-
-
45449125925
-
Efficient implementation of essentially non-oscillatory shock-capturing schemes
-
C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys., 77 (1988), pp. 439-471.
-
(1988)
J. Comput. Phys
, vol.77
, pp. 439-471
-
-
SHU, C.-W.1
OSHER, S.2
-
35
-
-
0021513424
-
High resolution schemes using flux limiters for hyperbolic conservation laws
-
P.K. SWEBY, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21 (1984), pp. 995-1011.
-
(1984)
SIAM J. Numer. Anal
, vol.21
, pp. 995-1011
-
-
SWEBY, P.K.1
-
37
-
-
19044370217
-
High order finite difference WENO schemes with the exact conservation property for the shallow water equations
-
Y. XING AND C.-W. SHU, High order finite difference WENO schemes with the exact conservation property for the shallow water equations, J. Comput. Phys., 208 (2005), pp. 206-227.
-
(2005)
J. Comput. Phys
, vol.208
, pp. 206-227
-
-
XING, Y.1
SHU, C.-W.2
|