This review paper concerns the application of numerical methods of the Godunov type to the
computation of approximate solutions to free-surface gravity flows modelled under a shallow …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

Laboratory experiments of dam-break flows are extensively used in investigations of
geophysical flows involving flood waves, to provide insight into relevant aspects of the …

This practical guide provides the best introduction to large deformation material point
method (MPM) simulations for geotechnical engineering. It provides the basic theory …

This paper presents a well-balanced numerical scheme for simulating frictional shallow
flows over complex domains involving wetting and drying. The proposed scheme solves, in …

A novel scheme has been developed for data reconstruction within a Godunov-type method
for solving the shallow-water equations with source terms. In contrast to conventional data …

Urbanization and climate change are contributing to severe flooding globally, damaging
infrastructure, disrupting economies, and undermining human well-being. Approaches to …

Many natural terrains have complicated surface topography. The simulation of steep-fronted
flows that occur after heavy rainfall flash floods or as inundation from dyke breaches is …

This work examines the sudden erosional flow initiated by the release of a dam-break wave
over a loose sediment bed. Extended shallow-water equations are formulated to describe …

A model based on the finite-volume method is developed for unsteady, two-dimensional,
shallow-water flow over arbitrary topography with moving lateral boundaries caused by …