Three-dimensional elliptic grid generation with fully automatic boundary constraints

• Published in: Journal of computational physics Vol. 229; no. 17; pp. 5966 - 5979
• Main Author: Kaul, Upender K.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.08.2010; Elsevier
• Subjects: Aeroshell; Algebra; Boundaries; Canopy; Clustering; Computational techniques; Decay; Decay functions; Enhanced elliptic grid generation; Exact sciences and technology; Finite element method; Grid clustering; Grid generation; Inflatable Aerodynamic Decelerator (IAD); Mars Science Laboratory (MSL); Mathematical analysis; Mathematical methods in physics; Mathematical models; Orthogonal grids; Physics; Single-zone grids; Three-dimensional boundary constraints; Inflatable Aerodynamic Decelerator (IAD); Aeroshell; Single-zone grids; Mars Science Laboratory (MSL); Canopy; Three-dimensional boundary constraints; Orthogonal grids; Enhanced elliptic grid generation; Grid clustering; Decay functions; Generalized function; Calculation methods; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.04.028

A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart 1 US patent 7231329. 1 presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C 2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C 2 continuity destroys the grid clustering near the boundaries.