Reparametrization and Volume Mesh Generation for Computational Fluid Dynamics Using Modified Catmull-Clark Methods

• Published in: Mathematical Methods for Curves and Surfaces pp. 425 - 441
• Main Authors: Rom, Michael, Brakhage, Karl-Heinz
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: B-spline surfaces and volumes; block-structured volume mesh generation; computational fluid dynamics; modified Catmull-Clark subdivision; reparametrization
• ISBN: 3642543812; 9783642543814
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-54382-1_24

A new technique is presented for using the Catmull-Clark subdivision method, modified for modeling sharp creases, to generate volume meshes used in computational fluid dynamics. Given a target surface of arbitrary genus, e.g., defined by a collection of trimmed B-spline patches, which represents an object in a flow, a simple polyhedron is constructed roughly approximating this target surface. After one Catmull-Clark subdivision, the polyhedron exclusively consists of quadrilaterals and its Catmull-Clark limit surface can be pre-computed. Points of the limit surface are projected onto the target surface and the control points of the polyhedron are adjusted by approximating the projected points. An iterative process of alternating subdivisions, projections and approximations leads to a watertight mesh consisting of untrimmed surface patches matching the given target surface. By attaching an offset mesh and a far-field mesh, a block-structured volume mesh is obtained, being well-suited for adaptive flow solvers.