Related papers: Domain-Decomposed Lagrangian Data Assimilation for…
We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion…
Particle-laden effects in high-speed flows require a coupled Euler and Lagrangian prediction technique with varying fidelity of thermochemical models, depending on the simulation conditions of interest. This requirement makes the…
For a moving hypersurface in the flow of a nonautonomous ordinary differential equation in $n$-dimensional Euclidean spaces, the fluxing index of a passively-advected Lagrangian particle is the total number of times it crosses the moving…
We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong…
The size of sea ice floes in the marginal ice zone (MIZ) is a key factor influencing ice coverage, albedo, wave propagation, and ocean--atmosphere energy exchanges. Floe size can be observed by processing visual-range imagery from ships,…
In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data…
This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches…
The aim of this paper is to prove that a three dimensional Lagrangian flow which defines equatorially trapped water waves is dynamically possible. This is achieved by applying a mixture of analytical and topological methods to prove that…
We consider the relationship between Eulerian modal decompositions and Lagrangian coherent structures (LCSs). The model sensitivity framework developed by Kasz\'as and Haller (2020) is used to express data-driven modal representations of…
The aim of this paper is to introduce a finite element formulation within Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space Conservation Law} (SCL) for differential equations on time dependent domains. The novelty…
Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…
Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…
The explicit semi-Lagrangian method method for solution of Lagrangian transport equations as developed in [Natarajan and Jacobs, Computer and Fluids, 2020] is adopted for the solution of stochastic differential equations that is consistent…
In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…
Machine learning techniques have seen a tremendous rise in popularity in weather and climate sciences. Data assimilation (DA), which combines observations and numerical models, has great potential to incorporate machine learning and…
During the last few years discontinuous Galerkin (DG) methods have received increased interest from the geophysical community. In these methods the solution in each grid cell is approximated as a linear combination of basis functions.…
We present a filter stabilization technique for the mildly compressible Euler equations that relies on a linear or nonlinear indicator function to identify the regions of the domain where artificial viscosity is needed and determine its…
Numerical simulations of the air in the atmosphere and water in the oceans are essential for numerical weather prediction. The state-of-the-art for performing these fluid simulations relies on an Eulerian viewpoint, in which the fluid…
An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit…
We introduce a framework for Data Assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data,…