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We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated…
In this introductory work I will present the Finite Difference method for hyperbolic equations, focusing on a method which has second order precision both in time and space (the so-called staggered leapfrog method) and applying it to the…
The vortex-wave system is a model for the evolution of 2D incompressible fluids in which the vorticity is split into a finite sum of Dirac masses plus an Lp part. Existence of a weak solution for this system was recently proved by Lopes…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…
We conduct direct numerical simulations of developed turbulence in a periodic cube to investigate the formation mechanism of the power spectral density of the Lagrangian velocity. We compare the power spectral density of the Lagrangian…
Robust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near-steady reference frames for vortex extraction, which…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
In this paper we derive the equations of motion for two-layer point vortex motion on the upper half plane. We study the invariants using symmetry, including the Hamiltonian and show that the two vortex problem is integrable. We characterize…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…
Hydrokinetic flapping foil turbines in swing-arm mode have gained considerable interest in recent years because of their enhanced capability to extract power, and improved efficiency compared to foils in simple mode. The performance of foil…
Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling…
We apply the local discontinuous Galerkin (LDG for short) method to solve a mixed boundary value problems for the Helmholtz equation in bounded polygonal domain in 2D. Under some assumptions on regularity of the solution of an adjoint…
The vorticity dynamics of the two-dimensional (2D) Taylor-Green vortex (TGV) problem is investigated in its multi-cellular configuration by solving the incompressible Navier-Stokes equation for long time intervals using a pseudo-spectral…
We propose an enhanced wall-boundary treatment for the lattice Boltzmann method (LBM), designed for high-Reynolds-number turbulent flows on adaptively refined Cartesian grids. The method improves the slip-velocity bounce-back scheme by…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
We report a Lagrangian study on the evolution of material surfaces in the K-type temporal transitional channel flow. Based on the Eulerian velocity field from the DNS, a backward-particle-tracking method is applied to solve the transport…
Unstable shear layers in environmental and industrial flows roll up into a series of vortices, which often form complex nonlinear merging patterns like pairs and triplets. These patterns crucially determine the subsequent turbulence, mixing…
We introduce a new Lagrangian particle tracking algorithm that tracks particles in three dimensions to separations between trajectories approaching contact. The algorithm also detects low Weber number binary collisions that result in…