Very high order WENO schemes using efficient smoothness indicators
| Autor: | Conghai Wu, Hu Li, Ling Wu, Shuhai Zhang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Floating point Smoothness (probability theory) Physics and Astronomy (miscellaneous) Applied Mathematics Stability (learning theory) Classification of discontinuities Computer Science Applications Euler equations Computational Mathematics Range (mathematics) Nonlinear system symbols.namesake Modeling and Simulation symbols Applied mathematics Node (circuits) Mathematics |
| Zdroj: | Journal of Computational Physics. 432:110158 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2021.110158 |
| Popis: | Very high order weighted essentially non-oscillatory (WENO) schemes can obtain more accurate results than those relatively low order WENO schemes for many problems. However, as the order increases, the candidate sub-stencils of WENO schemes will contain more node points. Then, the classical smoothness indicators become very complex and need much more floating point operations. Although they could be written in a more succinct form which is a sum of perfect squares, only a little improvement of the computational efficiency is obtained. Furthermore, for the power parameter p in the nonlinear weights of the previous (2r-1)th order WENO schemes, only the range of choices is given and the optimal value could be problem dependent. In this article, another class of very high order WENO schemes is constructed by using more efficient smoothness indicators. Compared with very high order WENO schemes using classical smoothness indicators, the new ones are more time efficient, and less error prone for programming. Furthermore, they have the same approximate dispersion relation (ADR) as their underlying linear schemes. And a more important advantage is that they have both good behavior near critical points and good stability near discontinuities. For Euler equations, a predetermined order reduction technique including two inequalities is proposed to deal with the problems caused by interactions between discontinuities of different characteristic fields. One inequality is constructed using this kind of smoothness indicators of pressure to suppress the non-physical oscillations. And the other is proposed according to the governing equation of the pressure to prevent the emergence of negative pressure. Several test problems are presented to demonstrate the good properties of the proposed WENO schemes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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