Related papers: LEMDA: A Lagrangian-Eulerian Multiscale Data Assim…
Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…
Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical…
Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterised by statistical stationarity or limited temporal…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincar\'e (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then derive a set of approximate…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
The use of large-scale multifaceted data is common in a wide variety of scientific applications. In many cases, this multifaceted data takes the form of a field-based (Eulerian) and point/trajectory-based (Lagrangian) representation as each…
We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when…
These lectures notes give an introduction to the fast developing area of research dealing with perturbative descriptions of the gravitational instability in an expanding universe. I just sketch the outlines of some proofs, and many…
Lagrangian averaging is a valuable tool for the analysis and modelling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by…
Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on…
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle,…
Multivariate Gaussian processes (GPs) offer a powerful probabilistic framework to represent complex interdependent phenomena. They pose, however, significant computational challenges in high-dimensional settings, which frequently arise in…
An explicit high order semi-Lagrangian method is developed for solving Lagrangian transport equations in Eulerian-Lagrangian formulations. To ensure a semi-Lagrangian approximation that is consistent with an explicit Eulerian, discontinuous…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
We focus on Partial Differential Equation (PDE) based Data Assimilatio problems (DA) solved by means of variational approaches and Kalman filter algorithm. Recently, we presented a Domain Decomposition framework (we call it DD-DA, for…
We present a computational framework for modeling large-scale particle-laden flows in complex domains with the goal of enabling simulations in medical-image derived patient specific geometries. The framework is based on a volume-filtered…