Geodesic
Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the CABARET scheme
Matematičeskoe modelirovanie, Tome 35 (2023) no. 3, pp. 79-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to the extension of the multilayer hydrostatic model CABARETMFSH 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$\times$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 threedimensional fluid flow with a variable density is used. The numerical calculations are in satisfactory agreement with experimental data.
Keywords: numerical methods, stratified flow, 3D experiments
Mots-clés : validation, CABARET scheme. 
@article{MM_2023_35_3_a4,
     author = {V. M. Goloviznin and Pavel A. Mayorov and Petr A. Mayorov and A. V. Solovjev},
     title = {Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the {CABARET} scheme},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {79--92},
     publisher = {mathdoc},
     volume = {35},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_3_a4/}
}
TY  - JOUR
AU  - V. M. Goloviznin
AU  - Pavel A. Mayorov
AU  - Petr A. Mayorov
AU  - A. V. Solovjev
TI  - Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the CABARET scheme
JO  - Matematičeskoe modelirovanie
PY  - 2023
SP  - 79
EP  - 92
VL  - 35
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2023_35_3_a4/
LA  - ru
ID  - MM_2023_35_3_a4
ER  - 
%0 Journal Article
%A V. M. Goloviznin
%A Pavel A. Mayorov
%A Petr A. Mayorov
%A A. V. Solovjev
%T Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the CABARET scheme
%J Matematičeskoe modelirovanie
%D 2023
%P 79-92
%V 35
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2023_35_3_a4/
%G ru
%F MM_2023_35_3_a4
V. M. Goloviznin; Pavel A. Mayorov; Petr A. Mayorov; A. V. Solovjev. Numerical modelling of three-dimensional variable-density flows by the multilayer hydrostatic model based on the CABARET scheme. Matematičeskoe modelirovanie, Tome 35 (2023) no. 3, pp. 79-92. http://geodesic.mathdoc.fr/item/MM_2023_35_3_a4/

[1] V. M. Goloviznin, A. Maiorov Pavel, A. Maiorov Petr, A. V. Solovjov, “New Numerical Algorithm for the Multi-Layer Shallow Water Equations Based on the Hyperbolic Decomposition and the CABARET Scheme”, Physical Oceanography, 26:6 (2019), 528–546 | DOI

[2] S. Karabasov, V. Goloviznin, “Compact Accurately Boundary-Adjusting High-Resolution Technique for fluid dynamics”, J. of Computational Physics, 228 (2009), 7426–7451 | DOI | MR

[3] J. E. Simpson, Gravity currents: In the environment and the laboratory, University press, Cambridge, 1999

[4] H. E. Huppert, “Gravity currents: a personal perspective”, J. of Fluid Mech., 554 (2006), 299–322 | DOI | MR

[5] C. Gladstone et al, “An experimental investigation of density-stratified inertial gravity currents”, Sedimentology, 51:4 (2004), 767–789 | DOI

[6] B. R. Sutherland et al, “Particle-bearing currents in uniform density and two-layer fluids”, Physical Review Fluids, 3:2 (2018), 023801 | DOI

[7] L. J. Marleau, M. R. Flynn, B. R. Sutherland, “Gravity currents propagating up a slope in a two-layer fluid”, Physics of Fluids, 27:3 (2015), 036601 | DOI

[8] M. Ungarish, T. Zemach, “On the slumping of high Reynolds number gravity currents in two-dimensional and axisymmetric configurations”, European J. of Mechanics-B/Fluids, 24:1 (2005), 71–90 | DOI | MR

[9] V. M. Goloviznin et al, “Validation of the low dissipation computational algorithm CABARET-MFSH for multilayer hydrostatic flows with a free surface on the lock-release experiments”, Journal of Computational Physics, 463 (2022), 111239 | DOI | MR

[10] R. Inghilesi et al, “Axisymmetric three-dimensional gravity currents generated by lock exchange”, Journal of Fluid Mechanics, 851 (2018), 507–544 | DOI | MR

[11] M. A. Hallworth, H. E. Huppert, M. Ungarish, “Axisymmetric gravity currents in a rotating system: experimental and numerical investigations”, J. of Fluid Mech., 447 (2001), 1–29 | DOI

[12] M. La Rocca et al, “Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom”, Physics of Fluids, 20:10 (2008), 106603 | DOI

[13] V. M. Goloviznin, M. A. Zaitsev, S. A. Karabasov, I. A. Korotkin, New CFD Algo-rithms for Multiprocessor Computer Systems, Moscow State University Press, M., 2013

[14] F. G. Serchi et al, “A numerical study of the triggering mechanism of a lock-release density current”, European Journal of Mechanics-B/Fluids, 33 (2012), 25–39 | DOI