Abstract
AbstractA set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.
Funder
Ministerio de Universidades
Conselleria de Cultura, Educación y Ciencia, Generalitat Valenciana
Universitat de Valencia
Publisher
Springer Science and Business Media LLC
Reference26 articles.
1. Amat, S., Ruiz-Alvarez, J., Shu, C.-W., Yáñez, D.F.: A new WENO-$$2r$$ Algorithm with progressive order of accuracy close to discontinuities. SIAM J. Numer. Anal. 58(6), 3448–3474 (2020)
2. Amat, S., Ruiz-Alvarez, J., Shu, C.-W., Yáñez, D.F.: Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing. App. Math. Comput. 403, 126131 (2021)
3. Aràndiga, F., Baeza, A., Belda, A.M., Mulet, P.: Analysis of WENO schemes for full and global accuracy. SIAM J. Numer. Anal. 49(2), 893–915 (2011)
4. Aràndiga, F., Baeza, A., Belda, A.M., Mulet, P.: Point-value WENO multiresolution applications to stable image compression. J. Sci. Comput. 43(2), 158–182 (2010)
5. Baeza, A., Bürger, R., Mulet, P., Zorío, D.: Central WENO schemes through a global average weight. J. Sci. Comput. 78, 499–530 (2019)