An advection velocity correction scheme for interface tracking using the level-set method

Abstract

An advection velocity correction (AVC) scheme for interface tracking using the level-set method is presented in this thesis. The key idea is to apply a correction to the interface advection velocity at points adjacent to the zero level-set, so as to enforce the preservation of the signed distance function property at these points. As such, the AVC scheme eliminates the need for explicit sub-cell x approaches, as reinitialization at points adjacent to the zero level-set is not needed. This ap- proach of correcting the advection velocity eld near the interface and computing the signed distance function (SDF) to a high order of accuracy near the interface, rather than applying an explicit sub-cell x during the reinitialization step repre- sents the key novel aspect of the AVC scheme. In this thesis results from using the AVC scheme along with advection and reinitialization schemes using upwind finite differencing on uniform meshes are presented. These results are determined for four canonical test problems: slotted disk rotation, deforming sphere, interacting circles and vortex in a box. These results are compared with corresponding results determined using a recently proposed explicit sub-cell x based reinitialization scheme (CR2). These comparisons show that the AVC scheme yields significantly improved conservation of enclosed volume/area within the interface. Note that, the present AVC scheme achieves this by only modifying velocity field values at mesh points. Therefore, the AVC algorithm can in principle be used within the framework of nearly any numerical scheme used to compute interface evolution us- ing the level-set method, even on non-uniform and unstructured meshes, in order to achieve improvements in solution quality.