Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A spatial-temporal weight analysis and novel nonlinear weights of weighted essentially non-oscillatory schemes for hyperbolic conservation laws (2310.05679v2)

Published 9 Oct 2023 in math.NA and cs.NA

Abstract: In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variation diminishing Runge-Kutta method. The rationale for the improved performance of the finite volume WENO-M, WENO-Z and WENO-ZR schemes over WENO-JS in the first time step is that the nonlinear weights corresponding to large errors are adjusted to increase the accuracy of numerical solutions. Based on this analysis, we propose novel Z-type nonlinear weights of the finite volume WENO scheme for hyperbolic conservation laws. Instead of taking the difference of the smoothness indicators for the global smoothness indicator, we employ the logarithmic function with tuners to ensure that the numerical dissipation is reduced around discontinuities while the essentially non-oscillatory property is preserved. The proposed scheme does not necessitate substantial extra computational expenses. Numerical examples are presented to demonstrate the capability of the proposed WENO scheme in shock capturing.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (35)
  1. J. Comput. Phys. 404, 109062 (2020)
  2. J. Sci. Comput. 72, 986–1020 (2017)
  3. J. Comput. Phys. 227(6), 3191–3211 (2008)
  4. J. Sci. Comput. 61, 343–368 (2014)
  5. Capdeville, G.: A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes. J. Comput. Phys. 227(5), 2977–3014 (2008)
  6. J. Comput. Phys. 466, 111398 (2022)
  7. J. Sci. Comput. 67, 1219–1246 (2016)
  8. Friedrich, O.: Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J. Comput. Phys. 144(1), 194–212 (1998)
  9. Math. Comp. 67(221), 73–85 (1998)
  10. Comput. Math. Appl. 134, 140–166 (2023)
  11. Appl. Numer. Math. 112, 27–50 (2017)
  12. J. Comput. Phys. 71(2), 231–303 (1987)
  13. J. Comput. Phys. 207(2), 542–567 (2005)
  14. J. Sci. Comput. 82, 76 (2020)
  15. J. Comput. Phys. 150(1), 97–127 (1999)
  16. Commun. Comput. Phys. 9(3), 627–648 (2011)
  17. J. Comput. Phys. 126(1), 202–228 (1996)
  18. Kolb, O.: On the full and global accuracy of a compact third order WENO scheme. SIAM J. Numer. Anal. 52(5), 2335–2355 (2014)
  19. SIAM J. Sci. Comput. 22(2), 656–672 (2000)
  20. J. Comput. Phys. 446, 110653 (2021)
  21. J. Sci. Comput. 88, 47 (2021)
  22. J. Comput. Phys. 115(1), 200–212 (1994)
  23. J. Comput. Phys. 183(1), 187–209 (2002)
  24. Comput. & Fluids 34(6), 642–663 (2005)
  25. J. Comput. Phys. 175(1), 108–127 (2002)
  26. Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: A. Quarteroni (ed.) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics, pp. 325–432. Springer, Berlin (1998)
  27. J. Comput. Phys. 77(2), 439–471 (1988)
  28. J. Comput. Phys. 83(1), 32–78 (1989)
  29. J. Comput. Phys. 201(1), 238–260 (2004)
  30. Commun. Comput. Phys. 8(3), 585–609 (2010)
  31. J. Comput. Phys. 473, 111758 (2023)
  32. Commun. Comput. Phys. 5(2-4), 836–848 (2009)
  33. J. Comput. Phys. 349, 220–232 (2017)
  34. J. Sci. Comput. 73, 1338–1359 (2017)
  35. SIAM J. Sci. Comput. 40(2), A903–A928 (2018)

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now