Lecture

Stochastic a-Navier-Stokes Model: Properties and Applications

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture by Ludovic Goudenège discusses the stochastic a-Navier-Stokes model, a simplified version of the Navier-Stokes equation for fluid dynamics. The model aims to be easier to simulate numerically while conserving physical properties. Various related works and models are explored, including numerical simulations and closure equations in Large Eddy Simulations. The lecture also covers the Galerkin approximation, assumptions, existence, and uniqueness of solutions, as well as exponential moments and invariant measures. Applications of the model in biological contexts are briefly mentioned, hinting at mathematical challenges posed by the Covid-19 crisis.

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics

Related concepts (32)

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Large eddy simulation

Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is currently applied in a wide variety of engineering applications, including combustion, acoustics, and simulations of the atmospheric boundary layer. The simulation of turbulent flows by numerically solving the Navier–Stokes equations requires resolving a very wide range of time and length scales, all of which affect the flow field.

Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Related lectures (64)

Viscous Beads Flowing Down a Vertical Fibre

Delves into the dynamics of fluid flowing down a vertical fibre, forming droplets under gravity and exhibiting various flow regimes.

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Turbulence Simulation and Models

Explores turbulence simulation, focusing on CFD, DNS, RANS, and LES.

Numerical Flow Simulation: Fundamentals

Covers the fundamentals of numerical flow simulation, emphasizing the importance of understanding the methodology and practicing simulation techniques to run full simulations autonomously.

Fluid Dynamics: Ideal Fluids