Performance Study of MUSCL Schemes Based on Different Numerical Fluxes

  • Dawei Sun


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.


MUSCL scheme Finite volume method Numerical flux 



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


  1. 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.MathSciNetCrossRefGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. 3.
    Kumar, S., & Singh, P. (2015). Higher-order MUSCL scheme for transport equation originating in a neuronal model. Oxford: Pergamon Press.Google Scholar
  4. 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.CrossRefMATHGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.MathSciNetCrossRefMATHGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. 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.MathSciNetCrossRefGoogle Scholar
  10. 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.MathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Physics and Electronic InformationInner Mongolia University for the NationalitiesTongliaoChina

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