Numerical resolution of well-balanced shallow water equations with complex source terms

By Qiuhua Liang, Fabien Marche. 2009

534 citations recorded by the source corpus.

Subfields: Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/dd4df3c94e072c5fccc757a4bdc6bfb84834c4a7

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In Computational Mechanics

1. Chi-Wang Shu
2. Yulong Xing
3. Songdong Shao
4. Soon Keat Tan
5. J. Pu
6. N. Cheng
7. Luke Smith
8. James T. Kirby

Citations in the corpus

• Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations (2013, methodology): “Both FUNWAVE-TVD and NHWAVE make use of a finite-volume TVD scheme, using a wellbalanced scheme for the pressure gradient following LIANG and MARCHE (2009).”
• A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case (2015, unknown): “[16] Liang, Q.”
• Towards a generalised GPU/CPU shallow-flow modelling tool (2013, methodology): “Validation of individual elements of the numerical scheme against analytical results for standard test cases can be found elsewhere in literature Liang (2010); Liang and Marche (2009), hence this section will focus on evaluating the performance benefits achieved through GPU processing.”
• A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation (2012, background): “The imbalance problem can be solved by a reformulation of this term in terms of deviations from an unforced but separately specified equilibrium state (see general derivations in Rogers et al., 2003 and recent application in Liang and Marche, 2009).”
• Source term treatment of SWEs using surface gradient upwind method (2012, methodology): “(2008) and Liang and Marche (2009) for the validation of their numerical schemes.”
• A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “There have been a number of positivity-preserving schemes [1, 5, 8, 15, 21, 32, 35] in the finite volume framework.”
• Shock-capturing non-hydrostatic model for fully dispersive surface wave processes (2012, methodology): “In this study, the method by Liang and Marche (2009) is employed.”
• A depth-averaged 2D shallow water model for breaking and non-breaking long waves affected by rigid vegetation (2012, methodology): “Brufau et al. (2002), Valiani et al. (2002), Begnudelli and Sanders (2006), Ying and Wang (2008), and Liang and Marche (2009) used approximate Riemann solvers and Schwanenberg and Harms (2004) and Lai and Khan (2012) used the discontinuous Galerkin method to solve the shallow water equations for…”