Godunov-type methods for free-surface shallow flows: A review
暂无分享,去创建一个
[1] R. Courant,et al. On the solution of nonlinear hyperbolic differential equations by finite differences , 1952 .
[2] J. J. Stoker. Water Waves: The Mathematical Theory with Applications , 1957 .
[3] I. Bohachevsky,et al. Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .
[4] J. Glimm. Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .
[5] G. Strang. On the Construction and Comparison of Difference Schemes , 1968 .
[6] B. V. Leer,et al. Towards the ultimate conservative difference scheme I. The quest of monotonicity , 1973 .
[7] J. Cunge,et al. Practical aspects of computational river hydraulics , 1980 .
[8] Randall J. LeVeque,et al. Large time step shock-capturing techniques for scalar conservation laws , 1981 .
[9] Numerical solutions to water waves generated by shallow underwater explosions , 1981 .
[10] Computational Aspects of the Random Choice Method for Shallow Water Equations , 1981 .
[11] Phillip Colella,et al. Glimm's Method for Gas Dynamics , 1982 .
[12] J. Monaghan. Why Particle Methods Work , 1982 .
[13] P. Lax,et al. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .
[14] D. Ouazar,et al. Computational Hydraulics , 1983 .
[15] S. F. Davis. TVD finite difference schemes and artificial viscosity , 1984 .
[16] James Glimm,et al. A generalized Riemann problem for quasi-one-dimensional gas flows , 1984 .
[17] P. Woodward,et al. The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .
[18] P. Sweby. High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .
[19] P. Colella. A Direct Eulerian MUSCL Scheme for Gas Dynamics , 1985 .
[20] Mutsuto Kawahara,et al. Finite element method for moving boundary problems in river flow , 1986 .
[21] P. Roe. CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .
[22] A New Numerical Technique for Quasi-Linear Hyperbolic Systems of Conservation Laws , 1986 .
[23] S. Osher,et al. Uniformly high order accuracy essentially non-oscillatory schemes III , 1987 .
[24] S. Osher,et al. Uniformly High-Order Accurate Nonoscillatory Schemes. I , 1987 .
[25] S. Osher,et al. Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .
[26] Paul Glaister,et al. An approximate linearised Riemann solver for the Euler equations for real gases , 1988 .
[27] C. Hirsch,et al. Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.
[28] Abioala A. Akanbi,et al. Model for Flood Propagation on Initially Dry Land , 1988 .
[29] Chi-Wang Shu,et al. TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework , 1989 .
[30] P. Roe. Remote boundary conditions for unsteady multi-dimensional aerodynamic computations , 1989 .
[31] Eleuterio F. Toro,et al. A weighted average flux method for hyperbolic conservation laws , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[32] C. Hirsch. Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows , 1990 .
[33] P. Colella. Multidimensional upwind methods for hyperbolic conservation laws , 1990 .
[34] Multi-dimensional schemes for scalar advection , 1991 .
[35] J. V. Soulis,et al. Computation of two-dimensional dam-break-induced flows , 1991 .
[36] Pilar García-Navarro,et al. 1‐D Open‐Channel Flow Simulation Using TVD‐McCormack Scheme , 1992 .
[37] Pilar García-Navarro,et al. Flux difference splitting for 1D open channel flow equations , 1992 .
[38] L. C. Wrobel. Numerical computation of internal and external flows. Volume 2: Computational methods for inviscid and viscous flows , 1992 .
[39] Prediction of supercritical flow in open channels , 1992 .
[40] S. Osher,et al. Triangle based adaptive stencils for the solution of hyperbolic conservation laws , 1992 .
[41] Eleuterio F. Toro,et al. The weighted average flux method applied to the Euler equations , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.
[42] Philip L. Roe,et al. A multidimensional generalization of Roe's flux difference splitter for the euler equations , 1993 .
[43] Pilar García-Navarro,et al. A HIGH-RESOLUTION GODUNOV-TYPE SCHEME IN FINITE VOLUMES FOR THE 2D SHALLOW-WATER EQUATIONS , 1993 .
[44] Alfredo Bermúdez,et al. Upwind methods for hyperbolic conservation laws with source terms , 1994 .
[45] D. Zhao,et al. Finite‐Volume Two‐Dimensional Unsteady‐Flow Model for River Basins , 1994 .
[46] E. Toro,et al. Restoration of the contact surface in the HLL-Riemann solver , 1994 .
[47] E. F. Toro,et al. The development of a Riemann solver for the steady supersonic Euler equations , 1994, The Aeronautical Journal (1968).
[48] T. Hou,et al. Why nonconservative schemes converge to wrong solutions: error analysis , 1994 .
[49] Improving the simulation of drying and wetting in a two-dimensional tidal numerical model , 1995 .
[50] P. García-Navarro,et al. Accurate flux vector splitting for shocks and shear layers , 1995 .
[51] Eleuterio F. Toro,et al. Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems , 1995 .
[52] Pilar García-Navarro,et al. Genuinely multidimensional upwinding for the 2D shallow water equations , 1995 .
[53] P. Raviart,et al. Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.
[54] Monika Wierse,et al. A new theoretically motivated higher order upwind scheme on unstructured grids of simplices , 1997, Adv. Comput. Math..
[55] Eleuterio F. Toro,et al. AOn WAF-Type Schemes for Multidimensional Hyperbolic Conservation Laws , 1997 .
[56] Derek M. Causon,et al. On the Choice of Wavespeeds for the HLLC Riemann Solver , 1997, SIAM J. Sci. Comput..
[57] A. Chorin. A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .
[58] E. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics , 1997 .
[59] Matthew Hubbard,et al. Conservative Multidimensional Upwinding for the Steady Two-Dimensional Shallow Water Equations , 1997 .
[60] A unified Riemann-probiem-based extension of the Warming–Beam and Lax–Wendroff schemes , 1997 .
[61] P. Roe. Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .
[62] E. F. Toro,et al. Primitive, Conservative and Adaptive Schemes for Hyperbolic Conservation Laws , 1998 .
[63] Randall J. LeVeque,et al. Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods , 1998 .
[64] M. Berzins,et al. An unstructured finite-volume algorithm for predicting flow in rivers and estuaries , 1998 .
[65] Jean-Antoine Désidéri,et al. Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes , 1998 .
[66] Matthew Hubbard,et al. Multidimensional Upwinding with Grid Adaptation , 1998 .
[67] M. Vázquez-Cendón. Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry , 1999 .
[68] A. A. Khan. Modeling flow over an initially dry bed , 2000 .
[69] P. García-Navarro,et al. On numerical treatment of the source terms in the shallow water equations , 2000 .
[70] B. Ben Moussa,et al. Convergence of SPH Method for Scalar Nonlinear Conservation Laws , 2000, SIAM J. Numer. Anal..
[71] Pilar García-Navarro,et al. Flux difference splitting and the balancing of source terms and flux gradients , 2000 .
[72] Eleuterio F. Toro,et al. Centred TVD schemes for hyperbolic conservation laws , 2000 .
[73] Mourad Heniche,et al. A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries , 2000 .
[74] E. Toro. Shock-Capturing Methods for Free-Surface Shallow Flows , 2001 .
[75] Pilar García-Navarro,et al. Efficient construction of high‐resolution TVD conservative schemes for equations with source terms: application to shallow water flows , 2001 .
[76] B. Moussa. Meshless Particle Methods: Recent Developments for Nonlinear Conservation Laws in Bounded Domain , 2001 .
[77] E. Toro. Godunov Methods: Theory and Applications , 2001 .
[78] Eleuterio F. Toro,et al. Towards Very High Order Godunov Schemes , 2001 .
[79] Pilar García-Navarro,et al. Balancing Source Terms and Flux Gradients in Finite Volume Schemes , 2001 .
[80] Robert J. Connell,et al. Two-Dimensional Flood Plain Flow. I: Model Description , 2001 .
[81] E. Toro,et al. Solution of the generalized Riemann problem for advection–reaction equations , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[82] Pilar García-Navarro,et al. Numerical Modeling of Basin Irrigation with an Upwind Scheme , 2002 .
[83] Claus-Dieter Munz,et al. ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D , 2002, J. Sci. Comput..
[84] Eleuterio F. Toro,et al. ARBITRARILY ACCURATE NON-OSCILLATORY SCHEMES FOR A NONLINEAR CONSERVATION LAW , 2002 .
[85] Scott F. Bradford,et al. Finite-Volume Model for Shallow-Water Flooding of Arbitrary Topography , 2002 .
[86] Eleuterio F. Toro,et al. ADER: Arbitrary High Order Godunov Approach , 2002, J. Sci. Comput..
[87] Eleuterio F. Toro,et al. PRICE: primitive centred schemes for hyperbolic systems , 2003 .
[88] Pilar García-Navarro,et al. Unsteady free surface flow simulation over complex topography with a multidimensional upwind technique , 2003 .
[89] Stephen Roberts,et al. Explicit schemes for dam-break simulations , 2003 .
[90] A. Colagrossi,et al. Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .
[91] Martin Käser,et al. Adaptive Methods for the Numerical Simulation of Transport Processes , 2003 .
[92] Michael Dumbser,et al. Fast high order ADER schemes for linear hyperbolic equations , 2004 .
[93] Luka Sopta,et al. Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations , 2004 .
[94] Eleuterio F. Toro,et al. CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS , 2004 .
[95] Pilar García-Navarro,et al. Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography , 2004 .
[96] Pilar García-Navarro,et al. Implicit schemes with large time step for non‐linear equations: application to river flow hydraulics , 2004 .
[97] Javier Murillo,et al. Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D , 2005 .
[98] Eleuterio F. Toro,et al. ADER schemes for three-dimensional non-linear hyperbolic systems , 2005 .
[99] Eleuterio F. Toro,et al. ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions , 2005 .
[100] Michael Dumbser,et al. ADER discontinuous Galerkin schemes for aeroacoustics , 2005 .
[101] Yulong Xing,et al. High order finite difference WENO schemes with the exact conservation property for the shallow water equations , 2005 .
[102] Armin Iske,et al. ADER schemes on adaptive triangular meshes for scalar conservation laws , 2005 .
[103] Javier Murillo,et al. Numerical boundary conditions for globally mass conservative methods to solve the shallow‐water equations and applied to river flow , 2006 .
[104] Manuel Jesús Castro Díaz,et al. High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems , 2006, Math. Comput..
[105] Javier Murillo,et al. Extension of an explicit finite volume method to large time steps (CFL>1): application to shallow water flows , 2006 .
[106] Jostein R. Natvig,et al. Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows , 2006, J. Comput. Phys..
[107] Carlos Parés Madroñal,et al. Numerical methods for nonconservative hyperbolic systems: a theoretical framework , 2006, SIAM J. Numer. Anal..
[108] Eleuterio F. Toro,et al. Derivative Riemann solvers for systems of conservation laws and ADER methods , 2006, J. Comput. Phys..
[109] M. J. Castro,et al. A parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products: Application to shallow flows , 2006 .
[110] With Invariant Submanifolds,et al. Systems of Conservation Laws , 2009 .