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Viscous Compressible Flow Solution using RBF Blended Interpolation

Michael F. Harris
University of Central Florida, Mechanical and Aerospace Engineering Dept., Orlando, FL

Alain J. Kassab
Department of Mechanical and Aerospace Engineering, University of Central Florida, 4000 Central Florida Blvd, Orlando, Florida, USA

Eduardo Divo
Department of Mechanical Engineering, Embry-Riddle Aeronautical University, 600 S Clyde Morris Blvd, Daytona Beach, Florida, USA

DOI: 10.1615/TFEC2018.cfd.022087
pages 71-79


KEY WORDS: compressible flow, meshless methods, Navier-Stokes Equations, radial basis functions

Abstract

Radial basis function interpolation can solve partial differential equations with spectral accuracy, especially when the field variables are smooth. However, the RBF interpolation is dependent on the shape parameter, c, which must be determined by trial and error or estimated. For smooth functions, the RBF is chosen to be a large value which renders the RBF flat producing highly accurate interpolation. This method tends to fail for steep gradients and discontinuities producing oscillations between nodes. A low shape parameter RBF interpolation tends to provide better results by suppressing the oscillations near shocks and discontinuities. A RBF blending scheme can be used to switch between low and high shape parameter interpolation to produce high accuracy in the smooth regions while capturing the steep gradients or shocks. This method is used to solve the compressible Navier-Stokes equations and results are presented in this paper.

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