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Within OpenFOAM, we develop a pressure-based solver for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe…

Fluid Dynamics · Physics 2023-02-10 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations…

Numerical Analysis · Mathematics 2024-05-01 Nicola Clinco , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

We consider three conservative forms of the mildly compressible Euler equations, called CE1, CE2 and CE3, with the goal of understanding which leads to the most accurate and robust pressure-based solver in a finite volume environment. Forms…

Fluid Dynamics · Physics 2024-02-29 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Over the past 30 years, the cell-centred finite volume method has developed to become a viable alternative to the finite element method in the field of computational solid mechanics. The current article presents an open-source toolbox for…

Numerical Analysis · Mathematics 2018-09-05 P. Cardiff , A. Karač , P. De Jaeger , H. Jasak , J. Nagy , A. Ivanković , Ž. Tuković

We introduce GAIA (Geospatial Artificial Intelligence for Atmospheres), a hybrid self-supervised geospatial foundation model that fuses Masked Autoencoders (MAE) with self-distillation with no labels (DINO) to generate semantically rich…

We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM(R), for flow and transport problems in highly heterogeneous geological media and other porous materials. The…

Numerical Analysis · Mathematics 2022-12-22 Matteo Icardi , Eugenio Pescimoro , Federico Municchi , Juan H Hidalgo

One of the prevailing challenges in Computational Fluid Dynamics is accurate simulation of two-phase flows involving heat and mass transfer across the fluid interface. This is currently an active field of research, which is to some extend…

Fluid Dynamics · Physics 2021-03-02 Henning Scheufler , Johan Roenby

We introduce ClimateMachine, a new open-source atmosphere modeling framework using the Julia language to be performance portable on central processing units (CPUs) and graphics processing units (GPUs). ClimateMachine uses a common framework…

In this work, we study the implementation of electrically-driven flow (EDF) models in the finite-volume framework of $\text{OpenFOAM}^\circledR$. The Poisson-Nernst-Planck model is used for the transport of charged species and it is coupled…

Fluid Dynamics · Physics 2018-09-06 Francisco Pimenta , Manuel A. Alves

A new OpenFOAM application to simulate multiphase flows in porous media is formulated and tested. The proposed solver combines the Eulerian multi-fluid formulation for a system of phase fractions with Darcy's law for flows through porous…

Our work is motivated by the analysis of ash plume dynamics, arising in the study of volcanic eruptions. Such phenomena are characterized by large Reynolds number (exceeding $10^7$) and a large number of polydispersed particles~[1]. Thus,…

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for…

Analysis of PDEs · Mathematics 2016-04-07 Jinkai Li , Edriss S. Titi

We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…

Numerical Analysis · Mathematics 2025-09-23 Marco Artiano , Oswald Knoth , Peter Spichtinger , Hendrik Ranocha

The dynamics of large eddies in the atmosphere and oceans is described by the surface quasi geostrophic equation, which is reminiscent of the Euler equations. Thermal fronts build up rapidly. Two different numerical methods combined with…

Numerical Analysis · Mathematics 2025-10-20 Peter Constantin , Qing Nie , Norbert Schorghofer

This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…

We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long simulations on an energy and enstrophy preserving…

Numerical Analysis · Mathematics 2012-05-10 Antonella Zanna

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…

Numerical Analysis · Mathematics 2020-01-08 Tommaso Benacchio , Rupert Klein

A new non-hydrostatic and cloud-resolving atmospheric model is developed for studying moist convection and cloud formation in planetary atmospheres. It is built on top of the Athena++ framework, utilizing its static/adaptive…

Earth and Planetary Astrophysics · Physics 2019-02-20 Cheng Li , Xi Chen

A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…

Fluid Dynamics · Physics 2015-05-26 Roberto Velasco-Segura , Pablo L. Rendón

We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…

Numerical Analysis · Mathematics 2020-12-16 Jonas P. Berberich , Roger Käppeli , Praveen Chandrashekar , Christian Klingenberg
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