Related papers: Grid-based calculation of Lagrangian mean
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
Considering turbulence is crucial to understanding clouds. However, covering all scales involved in the turbulent mixing of clouds with their environment is computationally challenging, urging the development of simpler models to represent…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
We introduce a new computational method for embedding Lagrangian sink particles into an Eulerian calculation. Simulations of gravitational collapse or accretion generally produce regions whose density greatly exceeds the mean density in the…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
We present a reduced basis technique for long-time integration of parametrized incompressible turbulent flows. The new contributions are threefold. First, we propose a constrained Galerkin formulation that corrects the standard Galerkin…
Given a fluid equation with reduced Lagrangian $l$ which is a functional of velocity $\MM{u}$ and advected density $D$ given in Eulerian coordinates, we give a general method for semidiscretising the equations to give a canonical…
Lagrangian tracer particles have long been used to track the history of individual gas parcels in hydrodynamical codes. Particles advected by the cell-centered velocity carry no representation of underlying numerical diffusion, and thus…
One issue associated with the use of Large-Eddy Simulation (LES) to investigate the dispersion of small inertial particles in turbulent flows is the accuracy with which particle statistics and concentration can be reproduced. The motion of…
We define and characterize multi-time Lagrangian structure functions using data stemming from two swirling flows with mean flow and turbulent fluctuations: A Taylor-Green numerical flow, and a von K\'arm\'an laboratory experiment. Data is…
Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…
We construct a family of explicit rotational solutions to the nonlinear governing equations for water waves, describing edge waves propagating over a plane-sloping beach. A detailed analysis of the edge wave dynamics and of the run-up…
Physical systems are commonly represented as a combination of particles, the individual dynamics of which govern the system dynamics. However, traditional approaches require the knowledge of several abstract quantities such as the energy or…
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters…