Conservative high-order-accurate finite-difference methods for curvilinear gridsTwo fourth-order-accurate finite-difference methods for numerically solving hyperbolic systems of conservation equations on smooth curvilinear grids are presented. The first method uses the differential form of the conservation equations; the second method uses the integral form of the conservation equations. Modifications to these schemes, which are required near boundaries to maintain overall high-order accuracy, are discussed. An analysis that demonstrates the stability of the modified schemes is also provided. Modifications to one of the schemes to make it total variation diminishing (TVD) are also discussed. Results that demonstrate the high-order accuracy of both schemes are included in the paper. In particular, a Ringleb-flow computation demonstrates the high-order accuracy and the stability of the boundary and near-boundary procedures. A second computation of supersonic flow over a cylinder demonstrates the shock-capturing capability of the TVD methodology. An important contribution of this paper is the dear demonstration that higher order accuracy leads to increased computational efficiency.
Document ID
19930061074
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Rai, Man M. (NASA Langley Research Center Hampton, VA, United States)
Chakrvarthy, Sukumar (Rockwell International Science Center Thousand Oaks, CA, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1993
Publication Information
Publication: In: AIAA Computational Fluid Dynamics Conference, 11th, Orlando, FL, July 6-9, 1993, Technical Papers. Pt. 2 (A93-44994 18-34)
Publisher: American Institute of Aeronautics and Astronautics