Skip to main content
SpringerLink
Log in

Numerical Modeling of Three-Dimensional Variable-Density Flows by the Multilayer Hydrostatic Model Based on the CABARET Scheme

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

This article considers the extension of the multilayer hydrostatic CABARET-MFSH model to the case of three spatial variables. The model describes the dynamics of a fluid with a variable density and a free surface. The hyperbolic decomposition algorithm gives a representation of the matrix of the system as a product of 4 × 4 matrices, the eigenvalues of each of which are always real. An explicit CABARET scheme is used to solve the system of hyperbolic equations in each layer. To validate the model, the problem of a three-dimensional fluid flow with variable density is used. The numerical calculations are in satisfactory agreement with the experimental data.

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

Access this article

Log in via an institution

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.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. V. M. Goloviznin, P. A. Maiorov, P. A. Maiorov, and A. V. Solovjev, “New numerical algorithm for the multi-layer shallow water equations based on the hyperbolic decomposition and the CABARET scheme,” Phys. Oceanogr. 26, 528–546 (2019).

    Article  Google Scholar 

  2. S. A. Karabasov and V. M. Goloviznin, “Compact Accurately Boundary-Adjusting high-REsolution Technique for fluid dynamics,” J. Comput. Phys. 228, 7426–7451 (2009). https://doi.org/10.1016/j.jcp.2009.06.037

    Article  MathSciNet  MATH  Google Scholar 

  3. J. E. Simpson, Gravity Currents in the Environment and the Laboratory (Cambridge University Press, Cambridge, 1999).

    Google Scholar 

  4. H. E. Huppert, “Gravity currents: a personal perspective,” J. Fluid Mech. 554, 299–322 (2006). https://doi.org/10.1017/S002211200600930X

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Gladstone, L. J. Ritchie, R. S. J. Sparks, and A. W. Woods, “An experimental investigation of density-stratified inertial gravity currents,” Sedimentology 51, 767–789 (2004). https://doi.org/10.1111/j.1365-3091.2004.00650.x

    Article  Google Scholar 

  6. B. R. Sutherland, M. K. Gingras, C. Knudson et al., “Particle-bearing currents in uniform density and two-layer fluids,” Phys. Rev. Fluids 3, 023801 (2018). https://doi.org/10.1103/PhysRevFluids.3.023801

    Article  Google Scholar 

  7. L. J. Marleau, M. R. Flynn, and B. R. Sutherland, “Gravity currents propagating up a slope in a two-layer fluid,” Phys. Fluids 27, 036601 (2015). https://doi.org/10.1063/1.4914471

    Article  Google Scholar 

  8. M. Ungarish and T. Zemach, “On the slumping of high Reynolds number gravity currents in two-dimensional and axisymmetric configurations,” Eur. J. Mech. – B/Fluids 24, 71–90 (2005). https://doi.org/10.1016/j.euromechflu.2004.05.006

    Article  MathSciNet  MATH  Google Scholar 

  9. V. M. Goloviznin, P. A. Maiorov, P. A. Maiorov, and A. V. Solovjev, “Validation of the low dissipation computational algorithm CABARET-MFSH for multilayer hydrostatic flows with a free surface on the lock-release experiments,” J. Comput. Phys. 463, 111239 (2022). https://doi.org/10.1016/j.jcp.2022.111239

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Inghilesi, C. Adduce, V. Lombardi et al., “Axisymmetric three-dimensional gravity currents generated by lock exchange,” J. Fluid Mech. 851, 507–544 (2018). https://doi.org/10.1017/jfm.2018.500

    Article  MathSciNet  Google Scholar 

  11. M. A. Hallworth, H. E. Huppert, and M. Ungarish, “Axisymmetric gravity currents in a rotating system: experimental and numerical investigations,” J. Fluid Mech. 447, 1–29 (2001). https://doi.org/10.1017/S0022112001005523

    Article  MATH  Google Scholar 

  12. M. La Rocca, C. Adduce et al., “Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom,” Phys. Fluids 20, 106603 (2008). https://doi.org/doi:10.1063/1.3002381

    Article  MATH  Google Scholar 

  13. V. M. Goloviznin, M. A. Zaitsev, S. A, Karabasov, and I. A. Korotkin, New CFD Algorithms for Multiprocessor Computer Systems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].

    Google Scholar 

  14. F. G. Serchi, J. Peakall et al., “A numerical study of the triggering mechanism of a lock-release density current,” Eur. J. Mech. – B/Fluids 33, 25–39 (2012). https://doi.org/10.1016/j.euromechflu.2011.12.004

    Article  MATH  Google Scholar 

Download references

Funding

This study was supported by the Russian Science Foundation (grant no. 18-11-00163) and was carried out at Moscow State University.

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    V. M. Goloviznin, Pavel A. Mayorov & Petr A. Mayorov

  2. Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia

    V. M. Goloviznin, Pavel A. Mayorov, Petr A. Mayorov & A. V. Solovjev

Authors
  1. V. M. Goloviznin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pavel A. Mayorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Petr A. Mayorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. V. Solovjev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pavel A. Mayorov.

Ethics declarations

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goloviznin, V.M., Mayorov, P.A., Mayorov, P.A. et al. Numerical Modeling of Three-Dimensional Variable-Density Flows by the Multilayer Hydrostatic Model Based on the CABARET Scheme. Math Models Comput Simul 15, 832–841 (2023). https://doi.org/10.1134/S2070048223050034

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048223050034

Keywords:

Search

Navigation