High-order well-balanced central WENO scheme for pre-balanced shallow water equations

Bermudez, 1994, Upwind methods for hyperbolic conservation laws with source terms, Comput Fluids, 23, 1049, 10.1016/0045-7930(94)90004-3 Greenberg, 1996, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J Numer Anal, 33, 1, 10.1137/0733001 Greenberg, 1997, Analysis and approximation of conservation laws with source terms, SIAM J Numer Anal, 34, 1980, 10.1137/S0036142995286751 Noelle S, Xing YL, Shu CW. High-order well-balanced schemes. In: Puppo G, Russo G, editors. Numerical methods for balance laws. Quaderni di Matematica; 2009. Xing, 2011, On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations, J Sci Comput, 48, 339, 10.1007/s10915-010-9377-y LeVeque, 1998, Balancing source terms and flux gradient on high-resolution Godunov methods: the quasi-steady wave-propagation algorithm, J Comput Phys, 146, 346, 10.1006/jcph.1998.6058 Vazquez-Cendon, 1999, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry, J Comput Phys, 148, 497, 10.1006/jcph.1998.6127 Jin, 2001, A steady state capturing method for hyperbolic systems with geometrical source terms, Math Model Numer Anal, 35, 631, 10.1051/m2an:2001130 Zhou, 2001, The surface gradient method for the treatment of source terms in the shallow-water equations, J Comput Phys, 168, 1, 10.1006/jcph.2000.6670 Rogers, 2003, Mathematical balancing of flux gradient and source terms prior to using Roe’s approximate Riemann solver, J Comput Phys, 192, 422, 10.1016/j.jcp.2003.07.020 Xing, 2005, High order finite difference WENO schemes with the exact conservation property for the shallow water equations, J Comput Phys, 208, 206, 10.1016/j.jcp.2005.02.006 Xing, 2006, High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms, J Sci Comput, 27, 477, 10.1007/s10915-005-9027-y Xing, 2006, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, J Comput Phys, 214, 567, 10.1016/j.jcp.2005.10.005 Xing, 2006, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Commun Comput Phys, 1, 100 Noelle, 2006, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows, J Comput Phys, 213, 474, 10.1016/j.jcp.2005.08.019 Kurganov, 2002, Central-upwind schemes for the saint-venant system, Math Model Numer Anal, 36, 397, 10.1051/m2an:2002019 Bryson, 2005, Balanced central schemes for the shallow water equations on unstructured grids, SIAM J Sci Comput, 27, 532, 10.1137/040605539 Caleffi, 2006, Fourth-order balanced source term treatment in central WENO schemes for shallow water equations, J Comput Phys, 218, 228, 10.1016/j.jcp.2006.02.001 Gallerano, 2011, Central WENO scheme for the integral form of contravariant shallow-water equations, Int J Numer Method Fluid, 67, 939, 10.1002/fld.2392 Liang, 2009, Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography, Comput Fluids, 38, 221, 10.1016/j.compfluid.2008.02.008 Levy, 1999, Central WENO schemes for hyperbolic systems of conservation laws, Math Model Numer Anal, 33, 547, 10.1051/m2an:1999152 Levy, 2000, A third order central WENO scheme for 2D conservation laws, Appl Numer Math, 33, 415, 10.1016/S0168-9274(99)00108-7 Levy, 2002, Compact central WENO schemes for multidimensional conservation laws, SIAM J Sci Comput, 22, 656, 10.1137/S1064827599359461 Levy, 2002, A forth-order central WENO schemes for multidimensional hyperbolic systems of conservation laws, SIAM J Sci Comput, 24, 480, 10.1137/S1064827501385852 Zennaro, 1986, Natural continuous extension of Runge–Kutta methods, Math Comput, 46, 119, 10.1090/S0025-5718-1986-0815835-1 Alcrudo, 2001, Exact solution to the Riemann problem of the shallow water equations with a bottom step, Comput Fluids, 30, 643, 10.1016/S0045-7930(01)00013-5 Benkhaldoun, 2007, Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes, J Comput Phys, 226, 180, 10.1016/j.jcp.2007.04.005 Noelle, 2007, High-order well-balanced finite volume WENO schemes for shallow water equation with moving water, J Comput Phys, 226, 29, 10.1016/j.jcp.2007.03.031 Vukovic, 2002, ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations, J Comput Phys, 179, 593, 10.1006/jcph.2002.7076