A conservative level-set/finite-volume method on unstructured grids based on a central interpolation scheme

Highlights: • Interface-capturing is based on a second-order unstructured finite-volume method. • A central interpolation technique is applied for cell-faces approximations. • The numerical method is quite suitable to work within the signed distance function. • 2D and 3D benchmarks validate the capabilities and performance of the algorithm. • The interface accurately returns to its original shape for the single vortex problem. In this paper, we introduce a second-order unstructured finite-volume method developed to solve a conservative level-set equation in two- and three-dimensional geometries. The characteristic function for the flow is defined at the center of each cell while the face-normal velocities are calculated at the mid-points of the corresponding cell faces. An interpolation method independent of cell shape and based on a central scheme is applied for the approximations at the cell faces. The capabilities and performance of the proposed scheme are validated using several 2D and 3D tests. Results show that the present numerical method is quite suitable for working within the smooth framework resulting from the signed distance function. Moreover, this method yields very accurate results in interface-capturing problems such as the single vortex deformation.