2021/10/13 by Martin Smuda, Florian Kummer · 10 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Basis function #Boundary (topology) #Computer science #Discontinuous Galerkin method #Discretization #Fast marching method #Finite element method #Flow (mathematics) #Fluid Dynamics and Heat Transfer #Geometry #Incompressible flow #Lattice Boltzmann Simulation Studies #Level set (data structures) #Level set method #Mathematical analysis #Mathematical optimization #Mathematics #Physics #Solver #Topology (electrical circuits)
paper · pdf · doi:10.1002/nme.6853
published in International Journal for Numerical Methods in Engineering 123(1), 197-225 (Wiley)
openalex publication_date 2021/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract 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.