Numerical method for solving unsteady axisymmetric problems of the hydrodynamics of an ideal liquid with free surfaces

Pressure and acceleration-induced distortion of an incompressible, inviscid liquid region is predicted numerically. The liquid is bounded by both fixed and free boundaries, and its motion is irrotational. Normal velocity is prescribed on fixed, though perhaps permeable boundaries, and the starting velocity potential is given on all free surfaces. Distortions of the liquid region are described by the motion of discrete kinematic markers assigned to each free surface. Problems are formulated on a square mesh computation field in terms of velocity potential. The liquid region interior is solved numerically by overrelaxation at every time step, which permits velocity components and potential rates to be calculated at the free surfaces. Marker positions and potentials are advanced each time step, thus preparing the computation field for further overrelaxation, and the process is repeated until finished. This technique was formulated as a Fortran IV computer program, FREESURF, for studying free surface motions. The technique can solve two-dimension rectangular or axisymmetric problems with fixed boundaries and up to three free surfaces. Bubble expansion and collapse near a free surface, dam break flows, draining of a tank, and other similar problems can be predicted with the method.

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A Numerical Method of Hankel Transform for Axisymmetric Problems of Elasticity

Bulletin of JSME ◽

10.1299/jsme1958.27.1333 ◽

1984 ◽

Vol 27 (229) ◽

pp. 1333-1338 ◽

Cited By ~ 1

Author(s):

Minoru HAMADA ◽

Koji KADOTA ◽

Jun KODAMA

Keyword(s):

Numerical Method ◽

Hankel Transform ◽

Axisymmetric Problems

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A method to measure pores and fissures in geologic materials under S.E.M. by digital image processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108209 ◽

1978 ◽

Vol 36 (1) ◽

pp. 212-213

Author(s):

L. Montoto ◽

M. Montoto ◽

A. Bel-Lan

Keyword(s):

Image Processing ◽

Optical Microscopy ◽

Digital Image Processing ◽

Digital Image ◽

Digital Processing ◽

Free Surfaces ◽

Geologic Materials ◽

Automatic Information ◽

Detector Output ◽

Rock Specimens

INTRODUCTION.- The physical properties of rock masses are greatly influenced by their internal discontinuities, like pores and fissures. So, these need to be measured as a basis for interpretation. To avoid the basic difficulties of measurement under optical microscopy and analogic image systems, the authors use S.E.M. and multiband digital image processing. In S.E.M., analog signal processing has been used to further image enhancement (1), but automatic information extraction can be achieved by simple digital processing of S.E.M. images (2). The use of multiband image would overcome difficulties such as artifacts introduced by the relative positions of sample and detector or the typicals encountered in optical microscopy.DIGITAL IMAGE PROCESSING.- The studied rock specimens were in the form of flat deformation-free surfaces observed under a Phillips SEM model 500. The SEM detector output signal was recorded in picture form in b&w negatives and digitized using a Perkin Elmer 1010 MP flat microdensitometer.

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Attractive mode force microscopy of chiral liquid crystal surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121740 ◽

1992 ◽

Vol 50 (1) ◽

pp. 268-269

Author(s):

B.D. Terris ◽

R. J. Twieg ◽

C. Nguyen ◽

G. Sigaud ◽

H. T. Nguyen

Keyword(s):

Liquid Crystal ◽

Crystal Surfaces ◽

Free Surfaces ◽

Control Range ◽

Force Microscopy ◽

Liquid Crystal Films ◽

Chiral Liquid Crystal ◽

Crystal Films ◽

Electrostatic Charging ◽

And Shifts

We have used a force microscope in the attractive, or noncontact, mode to image a variety of surfaces. In this mode, the microscope tip is oscillated near its resonant frequency and shifts in this frequency due to changes in the surface-tip force gradient are detected. We have used this technique in a variety of applications to polymers, including electrostatic charging, phase separation of ionomer surfaces, and crazing of glassy films.Most recently, we have applied the force microscope to imaging the free surfaces of chiral liquid crystal films. The compounds used (Table 1) have been chosen for their polymorphic variety of fluid mesophases, all of which exist within the temperature control range of our force microscope.

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