We propose the use of physics-informed neural networks for solving the shallow-water
equations on the sphere in the meteorological context. Physics-informed neural networks …

We introduce a physically relevant stochastic representation of the rotating shallow water
equations. The derivation relies mainly on a stochastic transport principle and on a …

The one-dimensional shallow water equations in Eulerian coordinates are considered.
Relations between symmetries and conservation laws for the potential form of the equations …

The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are
considered. It is shown the relationship between symmetries and conservation laws in …

We carry out the group classification of the class of two-dimensional shallow water
equations with variable bottom topography using an optimized version of the method of …

This paper provides a comprehensive derivation of the total energy equations for the
atmospheric components of Earth System Models (ESMs). The assumptions and …

We present a finite element variational integrator for compressible flows. The numerical
scheme is derived by discretizing, in a structure-preserving way, the Lie group formulation of …

We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and
helicity for three-dimensional incompressible Navier-Stokes equations. The discretization …

This paper presents a geometric variational discretization of compressible fluid dynamics.
The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie …

This article surveys research on the application of compatible finite element methods to
large-scale atmosphere and ocean simulation. Compatible finite element methods extend …