52 research outputs found
Efficient three-material PLIC interface positioning on unstructured polyhedral meshes
This paper introduces an efficient algorithm for the sequential positioning
(or nested dissection) of two planar interfaces in an arbitrary polyhedron,
such that, after each truncation, the respectively remaining polyhedron admits
a prescribed volume. This task, among others, is frequently encountered in the
numerical simulation of three-phase flows when resorting to the geometric
Volume-of-Fluid method. For two-phase flows, the recent work of Kromer & Bothe
(doi.org/10.1016/j.jcp.2021.110776) addresses the positioning of a single plane
by combining an implicit bracketing of the sought position with up to
third-order derivatives of the volume fraction. An analogous application of
their highly efficient root-finding scheme to three-material configurations
requires computing the volume of a twice truncated arbitrary polyhedron. The
present manuscript achieves this by recursive application of the Gaussian
divergence theorem in appropriate form, which allows to compute the volume as a
sum of quantities associated to the faces of the original polyhedron. With a
suitable choice of the coordinate origin, accounting for the sequential
character of the truncation, the volume parametrization becomes co-moving with
respect to the planes. This eliminates the necessity to establish topological
connectivity and tetrahedron decomposition after each truncation. After a
detailed mathematical description of the concept, we conduct a series of
carefully designed numerical experiments to assess the performance in terms of
polyhedron truncations. The high efficiency of the two-phase positioning
persists for sequential application, thereby being robust with respect to input
data and possible intersection topologies. In comparison to an existing
decomposition-based approach, the number of truncations was reduced by up to an
order of magnitude
Unstructured Grid Generation Techniques and Software
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop
Decoupling method for parallel Delaunay two-dimensional mesh generation
Parallel mesh generation procedures that are based on geometric domain decompositions require the permanent separators to be of good quality (in terms of their angles and length), in order to maintain the mesh quality. The Medial Axis Domain Decomposition, an innovative geometric domain decomposition procedure that addresses this problem, is introduced. The Medial Axis domain decomposition is of high quality in terms of the formed angles, and provides separators of small size, and also good work-load balance. It presents for the first time a decomposition method suitable for parallel meshing procedures that are based on geometric domain decompositions.;The Decoupling Method for parallel Delaunay 2D mesh generation is a highly efficient and effective parallel procedure, able to generate billions of elements in a few hundred of seconds, on distributed memory machines. Our mathematical formulation introduces the notion of the decoupling path, which guarantees the decoupling property, and also the quality and conformity of the Delaunay submeshes. The subdomains are meshed independently, and as a result, the method eliminates the communication and the synchronization during the parallel meshing. A method for shielding small angles is introduced, so that the decoupled parallel Delaunay algorithm can be applied on domains with small angles. Moreover, I present the construction of a sizing function, that encompasses an existing sizing function and also geometric features and small angles. The decoupling procedure can be used for parallel graded Delaunay mesh generation, controlled by the sizing function
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