We present a numerical scheme for axisymmetric solutions to curvature driven moving boundary problems governed by a local law of motion, e.g. the mean curvature flow, the surface diffusion flow, and the Willmore flow. We then present several numerical experiments for the Willmore flow. In particular, we provide numerical evidence that the Willmore flow can develop singularities in finite time.

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In [22], Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler an...

T HE life cycle of engineering design involves innovating to introduce a product, and when that is done, looking for ways to make itwork better. Supersonic aerodynamics can be looked atwith a similar perspective. Man has always wanted to fly faster. While the basicmechanics of supersonic flightwas laid out in the 1950s, people are yet to find ways in which to make Supersonic flight more efficie...

This paper studies a steady axisymmetric flow in a constricted rigid tube. A shear-thinning fluid modelling the deformation-dependent viscosity of the blood is proposed. The motion equation is written in vorticity-streamfunction formulation and is solved numerically by a finite difference scheme. The flow pattern with the distributions of pressure and shear stress at the wall are computed. The ...

Front tracking has proved to be an accurate and efficient algorithm in the sense that tracking the interface can reduce the error significantly [9,10]. By applying this algorithm, we conduct numerical simulations of Richtmyer–Meshkov (RM) instabilities in spherical geometry for axisymmetric flow. We demonstrate scaling invariance with respect to shock Mach number for fluid mixing statistics, su...

We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes’ stream-function are satisfied exactly. The veloci...

Abstract In order to improve the validity of bottom hole pressure model, and simplify its calculation process, a mathematical model instantaneous for unsteady flow was established by considering crossflow between fractures matrix. Different conditions, including reservoir top has constant pressure, were considered. The basis obtaining is solve diffusivity equation with integration axisymmetric ...

Non-axisymmetric simulations verify and extend the results from a previous linear Floquet stability analysis of the wakes of rings. The wakes corresponding to the saturated state of each predicted non-axisymmetric instability mode over the entire aspect ratio range are successfully computed, and isosurface plots are presented elucidating the vortical wake structures. The existence of three non-...

An axisymmetric full Navier-Stokes computational fluid dynamics study is conducted to examine nozzle exhaust jet plume effects on the sonic boom signature of a supersonic aircraft. A simplified axisymmetric nozzle geometry, representative of the nozzle on the NASA Dryden NF-15B Lift and Nozzle Change Effects on Tail Shock research airplane, is considered. The computational fluid dynamics code i...

Additional experiments with the slowly varying axisymmetric hurricane model described by Anthes are presented. Variable horizontal eddy viscosity coefficients are utilized to study circulations that result from an increased heating function and a heating function with a double maximum along the radial direction. Infrared radiative cooling is modeled for the clear tropical atmosphere following S...