Related papers: Moment Approximations and Model Cascades for Shall…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of…
We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description in the conformal relaxation time approximation, in order to determine the range of applicability of an effective description in…
Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based…
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a…
In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a…
This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of…
The shallow shelf approximation is a better ``sliding law'' for ice sheet modeling than those sliding laws in which basal velocity is a function of driving stress. The shallow shelf approximation as formulated by \emph{Schoof} [2006a] is…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
Salmon's nearly geostrophic model for rotating shallow-water flow is derived in full spherical geometry. The model, which results upon constraining the velocity field to the height field in Hamilton's principle for rotating shallow-water…
Knowing the sea surface velocity field is essential for various applications, such as search and rescue operations and oil spill monitoring, where understanding the movement of objects or substances is critical. However, obtaining an…
One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, known in the atmospheric community as the dynamical core. As…
Moment equations offer a compelling alternative to the kinetic description of plasmas, gases, and liquids. Their simulation requires fewer degrees of freedom than phase space models, yet it can still incorporate kinetic effects to a certain…
Free-surface flow is relevant to many researchers in water resources engineering, geohazard assessment, as well as coastal and river engineering. Many different free-surface models have been proposed, which span modeling complexity from the…
The Sllod equations of motion enable modeling of homogeneous flow at the atomic scale, and are commonly used to predict fluid properties such as viscosity. However, few publicly available codes support such simulations, and those that do…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…