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| Title: | High-order CESE schemes | Authors: | Wen, CY Jiang, Y Shi, L |
Issue Date: | 2023 | Source: | In CY Wen, Y Jiang, & L Shi (2023), Space-time conservation element and solution element method: advances and applications in engineering sciences, p. 57-68. Singapore: Springer. | Abstract: | This chapter is dedicated to the description of high-order CESE schemes. In the second-order CESE schemes, the first-order Taylor expansion was employed to approximate the unknowns and fluxes within the solution elements. The accuracy of the scheme mainly depends on the approximations on the surfaces of the conservation elements. Analogously, the high-order CESE schemes with Mth-order in space and time are generally derived from (M−1)th-order Taylor expansions in the solution elements. The high-order CESE schemes use a highly compact stencil. Furthermore, spatial and temporal high-order accuracy can be achieved simultaneously. We shall start with constructing a 1D high-order scheme and then extend it to multi-dimensional schemes. | Publisher: | Springer | ISBN: | 978-981-99-0875-2 (Hardcover) 978-981-99-0878-3 (Softcover) 978-981-99-0876-9 (eBook) |
DOI: | 10.1007/978-981-99-0876-9_5 | Rights: | © The Editor(s) (if applicable) and The Author(s) 2023. This book is an open access publication. This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The following publication Wen, CY., Jiang, Y., Shi, L. (2023). High-Order CESE Schemes. In: Space–Time Conservation Element and Solution Element Method. Engineering Applications of Computational Methods, vol 13. Springer, Singapore is available at https://doi.org/10.1007/978-981-99-0876-9_5. |
| Appears in Collections: | Book Chapter |
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