This paper presents an extensive review of most of the existing TVD schemes found in
literature that are based on the One-step Time–space-coupled Unsteady TVD criterion (OTU …

Climate change is expected to result in an increase in the frequency and intensity of extreme
weather events. In turn, this will result in more frequent occurrences of extreme flood events …

The aim of this paper is to present a novel monotone upstream scheme for conservation law
(MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to …

This article reviews the mathematical formulations of the depth‐integrated advection‐
diffusion equation used so far for modeling scalar transport and mixing in shallow …

Wildfires are becoming a global natural disaster under climate change. A worthwhile
concern is that the rainfall thresholds that trigger debris flows in catchments affected by …

Flood risk assessment is generally studied using flood simulation models; however, flood
risk managers often simplify the computational process; this is called a “simplification …

This paper derives a novel formulation of the depth-averaged shallow water equations with
anisotropic porosity for computational efficiency reasons. The aim is to run simulations on …

This paper investigates the relationship between the rainfall and runoff in idealised
catchments, either with or without obstacle arrays, using an extensively-validated fully …

This paper presents a high-resolution numerical method for solving mass transport problems
involving advection and anisotropic diffusion in shallow water based on unstructured mesh …

An efficient numerical scheme is developed for coupled hydrodynamic and scalar transport
systems to guarantee the conservation and the positivity-preserving properties for water …