Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T21:29:22.042Z Has data issue: false hasContentIssue false
  • English
  • Français

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:fengrz@buaa.edu.cn
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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