Reducing volume and shape errors in front tracking

Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, we propose a divergence-preserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared with other common interpolation methods. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation. Results of representative test-cases are presented, which demonstrate that the proposed methods can conserve the volume and shape of the front up to an order of magnitude better than conventionally used methods.