التفاصيل البيبلوغرافية
العنوان: |
Why Stable Finite-Difference Schemes Can Converge to Different Solutions: Analysis for the Generalized Hopf Equation. |
المؤلفون: |
Shargatov, Vladimir A., Chugainova, Anna P., Kolomiytsev, Georgy V., Nasyrov, Irik I., Tomasheva, Anastasia M., Gorkunov, Sergey V., Kozhurina, Polina I. |
المصدر: |
Computation; Apr2024, Vol. 12 Issue 4, p76, 15p |
مصطلحات موضوعية: |
RIEMANN-Hilbert problems, EQUATIONS |
مستخلص: |
The example of two families of finite-difference schemes shows that, in general, the numerical solution of the Riemann problem for the generalized Hopf equation depends on the finite-difference scheme. The numerical solution may differ both quantitatively and qualitatively. The reason for this is the nonuniqueness of the solution to the Riemann problem for the generalized Hopf equation. The numerical solution is unique in the case of a flow function with two inflection points if artificial dissipation and dispersion are introduced, i.e., the generalized Korteweg–de Vries-Burgers equation is considered. We propose a method for selecting coefficients of dissipation and dispersion. The method makes it possible to obtain a physically justified unique numerical solution. This solution is independent of the difference scheme. [ABSTRACT FROM AUTHOR] |
|
Copyright of Computation is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
قاعدة البيانات: |
Complementary Index |