This paper presents a state of the art on port-Hamiltonian formulations for the modeling and
numerical simulation of open fluid systems. This literature review, with the help of more than …

We present a novel asymptotic-preserving semi-implicit finite element method for weakly
compressible and incompressible flows based on compatible finite element spaces. The …

An accurate data-based prediction of the long-term evolution of Hamiltonian systems
requires a network that preserves the appropriate structure under each time step. Every …

We construct a structure-preserving finite element method and time-stepping scheme for
inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves …

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

In this article we propose two finite-element schemes for the Navier–Stokes equations,
based on a reformulation that involves differential operators from the de Rham sequence …

We construct finite element methods for the incompressible magnetohydrodynamics (MHD)
system that precisely preserve the magnetic and cross helicity, the energy law and the …

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

Numerical methods for the simulation of transient systems with structure-preserving
properties are known to exhibit greater accuracy and physical reliability, in particular over …

Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of
dynamical systems deliver physically relevant results. In this paper, we construct a structure …