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High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

Published online by Cambridge University Press:  20 August 2015

Renzhong Feng
Renzhong Feng*
Affiliation:
School of Mathematics and Systematic Science & Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
*
*Corresponding author.Email address:[email protected]
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Abstract

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes.

Keywords

65M9982D3782-08Cubic-Polynomial Interpolation schemehyperbolic equationstriangular mesh
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1588 - 1602
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Yabe, T. and Takei, E., A new higher-order Godunov method for general hyperbolic equations, J. Phys. Soc. Japan, 57(8) (1988), 2598–2601.Google Scholar
[2]Yabe, T., Ishikawa, T., Wang, P. Y., Aoki, T. and Kadota, Y., Cubic-polynomial interpolation. II. Two-and three-dimensional solvers, Comput. Phys. Commun., 66 (1991), 233–242.CrossRefGoogle Scholar
[3]Yabe, T., Xiao, F. and Utsumi, T., The constrained interpolation profile method for multiphase analysis, J. Comput. Phys., 169 (2001), 556–593.Google Scholar
[4]Shiraishi, K. and Matsuoka, T., Wave propagation simulation using the CIP method of characteristic equations, Commun. Comput. Phys., 3(1) (2008), 121–135.Google Scholar
[5]Nakamura, T., Tanaka, R., Yabe, T. and Takizawa, K., Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique, J. Comput. Phys., 174 (2001), 171–207.Google Scholar
[6]Yabe, T., Mizoe, H., Takizawa, K., Moriki, H., Im, H.-N. and Ogata, Y., Higher-order schemes with CIP method and adapitve Soroban grid towards mesh-free scheme, J. Comput. Phys., 194 (2004), 57–77.Google Scholar
[7]Liu, Y., Central schemes on overlapping cells, J. Comput. Phys., 209 (2005), 82–104.Google Scholar
[8]Liu, Y., Shu, C.-W., Tadmor, E. and Zhang, M., Non-oscillatory hierarchical reconstruction for central and finite volume schemes, Commun. Comput. Phys., 2 (2007), 933–963.Google Scholar
[9]Hu, G., Li, R. and Tang, T., A robust WENO type finite volume solver for steady Euler equations on unstructured grids, Commun. Comput. Phys., 9 (2011), 627–648.Google Scholar
[10]Mishra, S. and Tadmor, E., Constraint preserving schemes using potential-based fluxes. I. Multidimensional transport equations, Commun. Comput. Phys., 9 (2011), 688–710.Google Scholar
[11]Rabut, C., Multivariate divided difference with simple knots, SIAM J. Numer. Anal., 38(4) (2001), 1294–1311.Google Scholar
[12]Feng, R. and Zhou, X., A kind of multiquadric quasi-interpolation opertors satisfying any degree polynomial reproduction property to scattered data, J. Comput. Appl. Math., 235 (2011), 1502–1514.CrossRefGoogle Scholar