A symmetric formulation for computing transient shallow water flows

Guillermo Hauke1
1Departamento de Mecanica de Fluidos, Centro Politecnico Superior, C/Maria de Luna 3, 50015 Zaragoza, Spain

Tài liệu tham khảo

Shakib, 1991, A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 89, 141, 10.1016/0045-7825(91)90041-4 Hansbo, 1991, Adaptive streamline diffusion methods for compressible flow using conservation variables, Comput. Methods Appl. Mech. Engrg., 87, 267, 10.1016/0045-7825(91)90008-T Aliabadi, 1992, SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulation, University of Minnesota Supercomputer Institute Research Report UMSI 92/136 Le Beau, 1993, SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Comput. Methods Appl. Mech. Engrg., 104, 397, 10.1016/0045-7825(93)90033-T Soulaïmani, 1994, Finite element solution of compressible viscous flows using conservative variables, Comput. Methods Appl. Mech. Engrg., 118, 319, 10.1016/0045-7825(94)90006-X Hauke, 1995, A unified approach to compressible and incompressible flows and a new entropy-consistent k-epsilon model Hauke, 1994, A unified approach to compressible and incompressible flows, Comput. Methods Appl. Mech. Engrg., 113, 389, 10.1016/0045-7825(94)90055-8 Hauke, 1998, A comparative study of different sets of variables, Comput. Methods Appl. Mech. Engrg., 153, 1, 10.1016/S0045-7825(97)00043-1 Tadmor, 1984, Skew-selfadjoint form for systems of conservation laws, J. Math. Anal. Applic., 103, 428, 10.1016/0022-247X(84)90139-2 Harten, 1983, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49, 357, 10.1016/0021-9991(83)90136-5 Bova, 1996, An entropy variable formulation and applications for the two-dimensional shallow water equations, Int. J. Numer. Methods Fluids, 24, 29, 10.1002/(SICI)1097-0363(19960715)23:1<29::AID-FLD411>3.0.CO;2-U Abbott, 1992 Mock, 1980, Systems of conservation laws of mixed type, J. Diff. Eqns., 37, 70, 10.1016/0022-0396(80)90089-3 Hughes, 1986, A new finite element formulation for computational for computational fluid dynamics: III. The generalized streamline operator for multidimensional advection-diffusion systems, Comput. Methods Appl. Mech. Engrg., 73, 173, 10.1016/0045-7825(89)90111-4 Hughes, 1986, A new finite element formulation for computational fluid dynamics: IV. A discontinuity capturing operator for multidimensional advective-diffusion systems, Comput. Methods Appl. Mech. Engrg., 58, 329, 10.1016/0045-7825(86)90153-2 Shakib, 1991, A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms, Comput. Methods Appl. Mech. Engrg., 87, 35, 10.1016/0045-7825(91)90145-V I. MacDonald, Test problems with analytic solutions for steady open channel flow, Numerical Analysis Report 6/94, Department of Mathematics, University of Reading. Belles, 1992, Experimental investigation of two-dimensional dam-break induced flows, J. Hydraulic Res., 30, 47, 10.1080/00221689209498946 Garcia-Navarro, 1995, Genuinely multi-dimensional upwinding for the 2D shallow water equations, J. Computat. Phys., 121, 79, 10.1006/jcph.1995.1180