Modified level set equation and its numerical assessment

Abstract

In the context of level set methods, the level set equation is modified by embedding a source term. The exact expression of this term is such that the eikonal equation is automatically satisfied, and also, this term is zero on the interface. Theoretically, it renders the reinitialization of level sets unnecessary, similarly to the extension velocity method. The exact expression of the source term makes also possible the derivation of its local approximate forms, of zero-, first- and higher-order accuracy. Application of those forms simplifies the realization of level set methods in comparison with the extension velocity method, but requires the return to the reinitialization procedure. Nevertheless, the advantage of local approximate forms of the proposed source term is that the number of reinitializations can be significantly reduced in comparison with the standard level set equation with the reinitialization procedure. Furthermore, with increasing the order of accuracy of approximation less number of reinitializations is needed. This leads to improvement of the interface resolution. The paper describes the new approach and an assessment of its performance in different test cases.