Liquid Surface Motion Induced by Acceleration and External Pressure

Abstract

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.