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

Open channel hydraulics

William C. Yager · Journal of the Franklin Institute · 1960 · 4.9K citations

Hydraulic Engineering, Hydraulics, Engineering +1

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

Amiram Harten, Peter D. Lax, Bram van Leer · SIAM Review · 1983 · 3.3K citations

Numerical Analysis, Unified Representation, Hyperbolic Conservation Law +7

Upwind methods for hyperbolic conservation laws with source terms

Alfredo Bermúdez, Ma Elena Vazquez · Computers & Fluids · 1994 · 1K citations

Numerical Analysis, Engineering, Hyperbolic Conservation Law +4

Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm

Randall J. LeVeque · Journal of Computational Physics · 1998 · 797 citations

Numerical Analysis, Engineering, Semi-implicit Method +11

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 · 460 citations

Numerical Analysis, Marine Hydrodynamics, Upwind Schemes +8