Adaptation and Surface Modeling for Cartesian Mesh Methods

摘要

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, esh 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) dat astructure 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 O(N log N) operations. Couting arguments are presented which as sess the number of isotropic Cartesian cells required to resolve a complex geometry in 3D. This evidence motivates an accuracy study using constant, linear,a nd quadratic reconstruction in the boudnary elements.