Multilevel error estimation and adaptive h-refinement for Cartesian meshes with embedded boundaries

M. J. Aftosmis, Marsha Berger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using τ-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 106 to 107 cells.

Original languageEnglish (US)
Title of host publication40th AIAA Aerospace Sciences Meeting and Exhibit
StatePublished - 2002
Event40th AIAA Aerospace Sciences Meeting and Exhibit 2002 - Reno, NV, United States
Duration: Jan 14 2002Jan 17 2002

Other

Other40th AIAA Aerospace Sciences Meeting and Exhibit 2002
CountryUnited States
CityReno, NV
Period1/14/021/17/02

Fingerprint

Error analysis
mesh
grids
truncation errors
modules
histogram
estimates
histograms
estimators
extrapolation
shock
Extrapolation
operators
parameter
cells
incorporation
indicator

ASJC Scopus subject areas

  • Space and Planetary Science
  • Aerospace Engineering

Cite this

Aftosmis, M. J., & Berger, M. (2002). Multilevel error estimation and adaptive h-refinement for Cartesian meshes with embedded boundaries. In 40th AIAA Aerospace Sciences Meeting and Exhibit

Multilevel error estimation and adaptive h-refinement for Cartesian meshes with embedded boundaries. / Aftosmis, M. J.; Berger, Marsha.

40th AIAA Aerospace Sciences Meeting and Exhibit. 2002.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Aftosmis, MJ & Berger, M 2002, Multilevel error estimation and adaptive h-refinement for Cartesian meshes with embedded boundaries. in 40th AIAA Aerospace Sciences Meeting and Exhibit. 40th AIAA Aerospace Sciences Meeting and Exhibit 2002, Reno, NV, United States, 1/14/02.
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