Adaptation and surface modeling for cartesian mesh methods

M. J. Aftosmis, J. E. Melton, M. J. Berger

Research output: Contribution to conferencePaperpeer-review


This paper documents recent developments in the construction of a three dimensional solution adaptive Cartesian mesh method for solving the Euler equations around complex configurations. The work focuses on the general issues of surface modeling, mesh adaptation, and surface boundary conditions which are topics common to all Cartesian mesh methods. The surface modeling requirements of a hierarchy of wall boundary treatments are identified. and a robust, fast, memory-efficient algorithm is presented for intersecting the Cartesian mesh with the surface geometry. An Alternating Digital Tree (ADT) data structure is presented which permits an individual Cartesian cell to be intersected with an arbitrary geometry in logarithmic time, and a complexity analysis shows that the entire surface modeling procedure may be completed in 0(N log AO operations. Counting arguments are presented which assess the number of isotropic Cartesian cells required to resolve a complex geometry in 3D. This evidence motivates an accuracy study using constant, linear, and quadratic reconstruction in the boundary elements. The order of accuracy of these boundary conditions is assessed using a model problem in 2D. This study suggests that the discretization error at the boundary may be reduced substantially but it is more difficult to improve the asymptotic behavior. In addition to discrete solutions for ONERA M6 and NACA 0012 test cases, numerical results arc presented for a complex High Wing Transport (HWT) model complete with pylons, engine nacelles, flaps, leading edge slats, spoiler and flap vane.

Original languageEnglish (US)
Number of pages11
StatePublished - 1995
Event12th Computational Fluid Dynamics Conference, 1995 - San Diego, United States
Duration: Jun 19 1995Jun 22 1995


Other12th Computational Fluid Dynamics Conference, 1995
Country/TerritoryUnited States
CitySan Diego

ASJC Scopus subject areas

  • General Engineering


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