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A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…
This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their…
This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are…
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the…
We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the…
We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface…
Many parts of biological organisms are comprised of deformable porous media. The biological media is both pliable enough to deform in response to an outside force and can deform by itself using the work of an embedded muscle. For example,…
In this paper, we present a novel meshfree framework for fluid flow simulations on arbitrarily curved surfaces. First, we introduce a new meshfree Lagrangian framework to model flow on surfaces. Meshfree points or particles, which are used…
This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct…
Statistical tools are crucial for studying and modeling turbulent flows, where chaotic velocity fluctuations span a wide range of spatial and temporal scales. Advances in image velocimetry, especially in tracking-based methods, now allow…
The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of…
At the heart of any method for computational fluid dynamics lies the question of how the simulated fluid should be discretized. Traditionally, a fixed Eulerian mesh is often employed for this purpose, which in modern schemes may also be…
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
In this paper, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in…
Lagrangian reduction by stages is used to derive the Euler-Poincar\'e equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists…