Related papers: LCS Tool : A Computational Platform for Lagrangian…
This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
The method of Lagrangian descriptors has been already applied in many different contexts, specially in geophysical flows. In this paper we analyze the performance of this methodology in incompressible flows. We demonstrate that barriers to…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
We analyse the flow organization of turbulent fountains in stratified media under different conditions, using three-dimensional finite-time Lyapunov exponents. The dominant Lagrangian coherent structures responsible for the transport…
We develop methods for detecting and predicting the evolution of coherent spatiotemporal patterns in incompressible time-dependent fluid flows driven by ergodic dynamical systems. Our approach is based on representations of the generators…
This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…
Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh--B\'{e}nard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number ${\rm Ra}=10^6$…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
Estimating reliable geometric model parameters from the data with severe outliers is a fundamental and important task in computer vision. This paper attempts to sample high-quality subsets and select model instances to estimate parameters…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…
The extraction of spatio-temporal coherence in high-dimensional, chaotic, non-linear dynamical systems, such as turbulent flows, remains a fundamental challenge in physics, mathematics and engineering. In this work, we employ Shannon…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier--Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed…
A model for the pseudo-turbulent Reynolds stress tensor in compressible flows through monodisperse particle clouds is developed based on data from particle resolved numerical simulations. This model extends previous models for the…
In this paper we consider the transport--Stokes system, which describes the sedimentation of particles in a viscous fluid in inertialess regime. We show existence of Lagrangian solutions to the Cauchy problem with $L^1$ initial data. We…
We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. This is the situation encountered, for example, when analyzing the dynamics of sufficiently small particles immersed in a turbulent fluid and…
Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport,…