A high-order explicit finite difference scheme is derived solving the shallow water equations.
The boundary closures are based on the diagonal-norm summation-by-parts (SBP) …

Linearisation is often used as a first step in the analysis of nonlinear initial boundary value
problems. The linearisation procedure frequently results in a confusing contradiction where …

Hydrodynamic model outputs are used in urban flood risk modelling, flood alert systems,
and Monte Carlo hazard assessment. This study tackles an under-explored challenge …

In this paper, we study a (3+ 1)-dimensional generalized shallow water wave equation with
variable coefficients, which describes the flow below a pressure surface in a fluid. We give …

We derive boundary conditions and estimates based on the energy and entropy analysis of
systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that …

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is
to show that different boundary conditions give different convergence rates of the variance of …

We present an energy/entropy stable and high order accurate finite difference (FD) method
for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form …

This paper presents a stable and highly accurate numerical tool for computing river flows in
urban areas, which is a first step towards a numerical tool for flood predictions. We start with …

This study provides numerical solutions to the two-dimensional linearized shallow water
equations (SWE) using a high-order finite difference scheme in Summation By Parts (SBP) …

We derive and analyse well-posed boundary conditions for the linear shallow water wave
equation. The analysis is based on the energy method and it identifies the number, location …