相关论文: The vortex method for 2D ideal flows in the exteri…

We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded divergence-free velocity field having bounded scalar curl. This…

The evolution of a vortex line following the binormal flow equation (i.e. with a velocity proportional to the local curvature in the direction of the binormal vector) has been postulated as an approximation for the evolution of vortex…

Vortex flows are ubiquitous in both natural processes and engineering applications, including phenomena such as typhoons, water currents, and aerospace fluid dynamics. The vortex particle method, a computational approach grounded in vortex…

It is shown that the Euler hydrodynamics for vortical flows of an ideal fluid coincides with the equations of motion of a charged {\it compressible} fluid moving due to a self-consistent electromagnetic field. Transition to the Lagrangian…

We consider the dynamics of a two-dimensional incompressible perfect fluid on a M\"obius strip embedded in $\mathbb{R}^3$. The vorticity-streamfunction formulation of the Euler equations is derived from an exterior-calculus form of the…

We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take into account the effect of external flow. We prove the unique…

In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow…

We introduce a novel boundary condition for incompressible Eulerian simulations formulated using a Biot-Savart vorticity integral that maintains high-accuracy results even when the domain boundary is within a body-length of immersed solid…

We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…

The point vortex model is an idealized model for describing the dynamics of many vortices with numerical efficiency, and has been shown to be powerful in modeling the dynamics of vortices in a superfluid. The model can be extended to…

We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector rather than the velocity. It enables a feasible Lagrangian study of fluid dynamics, as the isosurface of…

We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of vorticity from the fluid mass they enclose…

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…

Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates,…

We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity…

The point vortex dynamics in background fields on surfaces is justified as an Euler-Arnold flow in the sense of de Rham currents. We formulate a current-valued solution of the Euler-Arnold equation with a regular-singular decomposition. For…

We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vortices submitted to a small external stochastic perturbation…

We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable…

We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…

Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article we observe that the dynamics need not be trivial if one is willing to consider…