Skip to main content
Log in

Performance Study of MUSCL Schemes Based on Different Numerical Fluxes

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

The numerical flux is an important element in the numerical model for solving shallow water flow problems in MUSCL scheme. It is used to determine the normal transport through the boundary of the control body. With the TVD numerical flux, because of the simple form of Lax–Friedrichs, it is adopted in many articles. In fact, there are many different numerical fluxes based on exact Riemann solutions or approximate Riemann solutions, and these numerical fluxes can be combined with the MUSCL scheme. For the one-dimensional and two-dimensional shallow water equations, starting from the accuracy and discontinuous capture ability, a series of numerical examples are simulated based on the six different numerical fluxes with MUSCL scheme. Through the result analysis, the paper find out the numerical fluxes which are more suitable for shallow water flow combined with MUSCL scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Li, X. S., & Li, X. L. (2016). All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence. International Journal of Computational Fluid Dynamics, 30(1), 69–78.

    Article  MathSciNet  Google Scholar 

  2. Zingale, M., & Katz, M. P. (2015). On the piecewise parabolic method for compressible flow with stellar equations of state. Astrophysical Journal Supplement, 216(2), 1–30.

    Article  Google Scholar 

  3. Kumar, S., & Singh, P. (2015). Higher-order MUSCL scheme for transport equation originating in a neuronal model. Oxford: Pergamon Press.

    Google Scholar 

  4. Delis, A. I., & Skeels, C. P. (2015). TVD schemes for open channel flow. International Journal for Numerical Methods in Fluids, 26(7), 791–809.

    Article  MATH  Google Scholar 

  5. Hasan, M., Sultana, S., Andallah, L. S., et al. (2015). Lax–Friedrich scheme for the numerical simulation of a traffic flow model based on a nonlinear velocity density relation. American Journal of Computational Mathematics, 5(2), 186–194.

    Article  Google Scholar 

  6. Chiavassa, G., Martã, M. C., & Mulet, P. (2015). Hybrid WENO schemes for polydisperse sedimentation models. International Journal of Computer Mathematics, 93(11), 1801–1817.

    Article  MathSciNet  MATH  Google Scholar 

  7. Barth, A., Bürger, R., Kröker, I., et al. (2016). Computational uncertainty quantification for a clarifier–thickener model with several random perturbations: A hybrid stochastic Galerkin approach. Computers & Chemical Engineering, 89, 11–26.

    Article  Google Scholar 

  8. Zhang, M., Qiao, H., Xu, Y., et al. (2016). Numerical study of wave–current–vegetation interaction in coastal waters. Environmental Fluid Mechanics, 16(5), 1–17.

    Article  Google Scholar 

  9. Qian, Z., & Lee, C. H. (2015). HLLC scheme for the preconditioned pseudo-compressibility Navierâ Stokes equations for incompressible viscous flows. International Journal of Computational Fluid Dynamics, 29(6–8), 400–410.

    Article  MathSciNet  Google Scholar 

  10. Gjennestad, M. A., Gruber, A., Lervåg, K. Y., et al. (2017). Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme. Journal of Computational Physics, 348, 1–22.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the Scientific Research Foundation of Inner Mongolia University for Nationality No. NMDYB1782.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dawei Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, D. Performance Study of MUSCL Schemes Based on Different Numerical Fluxes. Wireless Pers Commun 102, 1763–1772 (2018). https://doi.org/10.1007/s11277-017-5234-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-5234-8

Keywords

Navigation