Weak solutions for partial differential equations with source terms: Application to the shallow water equations

On the solution of nonlinear hyperbolic differential equations by finite differences

Richard Courant, Eugene Isaacson, Mina Rees · Communications on Pure and Applied Mathematics · 1952 · 1K citations

Natural Sciences, Mathematics, Physics +11

The Surface Gradient Method for the Treatment of Source Terms in the Shallow-Water Equations

Jian Zhou, D. M. Causon, C. G. Mingham et al. · Journal of Computational Physics · 2001 · 542 citations

Natural Sciences, Earth Sciences, Oceanography +9

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

Qiuhua Liang, Fabien Marche · Advances in Water Resources · 2009 · 505 citations

Natural Sciences, Earth Sciences, Mathematics +14

Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry

M. Elena Vázquez-Cendón · Journal of Computational Physics · 1999 · 463 citations

Engineering, Hydrology, Ocean Engineering +13

Some exact solutions to the nonlinear shallow-water wave equations

W. C. Thacker · Journal of Fluid Mechanics · 1981 · 394 citations

Natural Sciences, Ocean Engineering, Oceanography +13