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A highly efficient finite volume method with a diffusion control parameter for hyperbolic problems

Author

Listed:
  • Aboussi, Wassim
  • Ziggaf, Moussa
  • Kissami, Imad
  • Boubekeur, Mohamed

Abstract

This article proposes a highly accurate, fast, and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of characteristics. The approach is simple to implement, has no entropy defect as seen in the numerical tests, and avoids solving Riemann problems. A diffusion control parameter is introduced to increase the accuracy of the scheme. Numerical examples are presented for the one-dimensional Euler equation for an ideal gas. The results demonstrate the method’s ability to capture contact discontinuity and shock wave profiles with high accuracy and low cost, as well as its robustness.

Suggested Citation

  • Aboussi, Wassim & Ziggaf, Moussa & Kissami, Imad & Boubekeur, Mohamed, 2023. "A highly efficient finite volume method with a diffusion control parameter for hyperbolic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 177-193.
    • Handle: RePEc:eee:matcom:v:213:y:2023:i:c:p:177-193
    DOI: 10.1016/j.matcom.2023.05.023
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