LAUSR

In this work a solver for two‐dimensional, instationary two‐phase flows on the basis of the extended discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This allows a subcell accurate representation of the incompressible Navier‐Stokes equations in their sharp interface formulation. The interface is described as the zero set of a signed‐distance level‐set function and discretized by a standard DG method. For the interface, resp. level‐set, evolution an extension velocity field is used and a two‐staged algorithm is presented for its construction on a narrow‐band. On the cut‐cells a monolithic elliptic extension velocity method is adapted and a fast‐marching procedure on the neighboring cells. The spatial discretization is based on a symmetric interior penalty method and for the temporal discretization a moving interface approach is adapted. A cell agglomeration technique is utilized for handling small cut‐cells and topology changes during the interface motion. The method is validated against a wide range of typical two‐phase surface tension driven flow phenomena in a 2D setting including capillary waves, an oscillating droplet and the rising bubble benchmark.