Free Surface

A large col­lec­tion of flu­id prob­lems in­volves mov­ing in­ter­faces. Ap­pli­ca­tions in­clude air-wa­ter dy­nam­ics, break­ing sur­face waves and sol­id bod­ies pen­e­trat­ing in flu­ids. In many such ap­pli­ca­tions, the in­ter­play be­tween the in­ter­face dy­nam­ics and the sur­round­ing flu­id mo­tion is sub­tle, with fac­tors such as den­si­ty ra­tios and tem­per­a­ture jumps across the in­ter­face, sur­face-ten­sion ef­fects, topo­log­i­cal con­nec­tiv­i­ty, and bound­ary con­di­tions play­ing sig­nif­i­cant roles in the dy­nam­ics.

The solver us­es a lev­el set method, a fast and re­li­able tech­nique in or­der to track and cor­rect­ly rep­re­sent mov­ing in­ter­faces. they re­ly on an im­plic­it rep­re­sen­ta­tion of the in­ter­face whose equa­tion of mo­tion is nu­mer­i­cal­ly ap­prox­i­mat­ed us­ing schemes built from those for hy­per­bol­ic-con­ser­va­tion laws. The re­sult­ing tech­niques are able to han­dle prob­lems in which the speed of the evolv­ing in­ter­face may sen­si­tive­ly de­pend on lo­cal prop­er­ties such as cur­va­ture and nor­mal di­rec­tion, as well as com­plex physics off the front and in­ter­nal jump and bound­ary con­di­tions de­ter­mined by the in­ter­face lo­ca­tion.
Lev­el set meth­ods are par­tic­u­lar­ly de­signed for prob­lems in mul­ti­ple space di­men­sions in which the topol­o­gy of the evolv­ing in­ter­face changes dur­ing the course of events and for prob­lems in which sharp cor­ners and cusps are present.