Related papers: On the 1D Modeling of Fluid Flowing through a Junc…
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
Slug flows are a typical intermittent two-phase flow pattern that can occur in submarine pipelines connecting the wells to the production facility and that is known to cause undesired consequences. In this context, computational fluid…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid $3$-dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated…
We consider two incidence problems for integral curves of vector fields. The first is an analogue of the Euclidean joints problem, in which lines are replaced by integral curves of smooth vector fields taken from some finite-dimensional…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
Compound flows consist of two or more parallel compressible streams in a duct and their theoretical treatment has gained attention for the analysis and modelling of ejectors. Recent works have shown that these flows can experience choking…
It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time (Ph. Serfati…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph…
This paper is concerned with coupling conditions at junctions for transport models which differ in their fidelity to describe transient flow in gas pipelines. It also includes the integration of compressors between two pipes with possibly…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
It is proven that the only incompressible Euler fluid flows with fixed straight streamlines are those generated by the normal lines to a round sphere, a circular cylinder or a flat plane, the fluid flow being that of a point source, a line…
The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…