Marić, Tomislav Lagrangian/Eulerian numerical methods for fluid interface advection on unstructured meshes. (English) Zbl 1447.76026 Darmstadt: TU Darmstadt, Fachbereich Mathematik (Diss.). xxvi, 212 p., open access (2017). From the author’s abstract:In this thesis two developed Lagrangian/Eulerian numerical methods are presented for advecting the sharp fluid interface between immiscible fluids: a dimensionally un-split geometrical Volume of Fluid methodand a coupled Level Set/Front Tracking method.Both numerical methods support solution domains are discretized with unstructured meshes.A new triangulation algorithm for congruent polyhedra is introduced that accurately decomposes polyhedra with non-convex faces into tetrahedra, allowing for a more accurate volume calculation.A novel simple reconstruction interface algorithm is developed that ensures second- order accuracy of the interface advection.A conservative error redistribution algorithm is developed that supports parallel execution and ensures volume conservation near machine tolerance, numerical stability and exact numerical boundedness of the solution.For the coupled Level Set/Front Tracking method, an efficient combination of octree and known vicinity search algorithms is proposed, for fast Front Tracking on unstructured meshes.An efficient and modular software library for 3D geometrical operations in the C++ programming language is developed, that significally simplifies the development of new transport algorithms. Developed algorithms are extended for parallel computation with the domain decomposition model. Reviewer: Titus Petrila (Cluj-Napoca) MSC: 76M99 Basic methods in fluid mechanics 65Z05 Applications to the sciences Keywords:Lagrangian numerical methods; Eulerian numerical methods; fluid inteface advection; volume-of-fluid method; flux polyhedron triangulation Software:KRAKEN; lentFoam; PROST; voFoam; OpenMPI; Boost; Gerris; CGAL; OpenFOAM PDFBibTeX XMLCite \textit{T. Marić}, Lagrangian/Eulerian numerical methods for fluid interface advection on unstructured meshes. Darmstadt: TU Darmstadt, Fachbereich Mathematik (Diss.) (2017; Zbl 1447.76026) Full Text: Link