CC BY
87. A. Klimova, E. Rondeau, K. Andersson, J. Porras, A. Rybin, and A. Zaslavsky,�An international Master�s program in
green ICT as a contribution to sustainable development, J. of Cleaner Production, vol. 135, pp. 223�239, 2016.
Simulations of viscous incompressible fluid flows on grids with unmatched interfaces in the LOGOS software
package
A. V. Korotkov, S. V. Lashkin, A. S. Kozelkov
FSUE �Russian Federal Nuclear Center � All-Russian Research Institute of Experimental Physics�, Sarov, Nizhny
Novgorod Region
Email: alvladkor79@mail.ru
DOI 10.24412/cl-35065-2021-1-01-73
At present, numerical simulations of industry-specific hydrodynamic and aerodynamic problems are based
on solving three-dimensional Navier-Stokes equations on arbitrary unstructured grids [1, 2]. Dividing complex
initial geometries into simpler fragments makes it easier to construct grid models and yields higher-quality
grids. Such grid models are usually composed of unmatched grid fragments. CFD simulations on this kind of
grids require special unmatched grid interfaces to be developed.
This paper describes a numerical method, which considers specific aspects of solving the Navier-Stokes
equations in viscous incompressible flow simulations in the vicinity of interfaces between unmatched arbitrary
unstructured grid fragments. The numerical method presented in this paper is implemented based on the Rus-
sian LOGOC software package [3]. Performance of this method is demonstrated by three-dimensional simula-
tions of a turbulent flow in a circular diffuser.
References
1. Pogosyan M.A., Savelievskikh E.P., Shagaliev R.M., Kozelkov A.S., Strelets D.Yu., Ryabov A.A., Kornev A.V., Deryugin
Yu.N., Spiridonov V.F., Tsiberev K.V. Application of Russian supercomputer technologies to develop the advanced models
of aviation technology // J. VANT, Ser. Mathematical Modeling of Physical Processes, 2013, issue 3, p. 3-17. [ In Russian].
2. Betelin V.B., Shagaliev R.M., Aksenov S.V., Belyakov I.M., Deryuguin Yu.N., Kozelkov A.S., Korchazhkin D.A., Nikitin
V.F., Sarazov A.V., Zelenskiy D.K. Mathematical simulation of hydrogen�oxygen combustion in rocket engines using
LOGOS code // Acta Astronautica 2014, v. 96, p.53�64.
3. Kozelkov A.S., Shagaliev R.M., Kurulin V.V., Yalozo A.V., Lashkin S.V. Analysis of supercomputer potential as applied
to hydrodynamic scalable numerical simulations in industrial applications // Computational Mathematics and
Mathematical Physics. 2016. V. 56. Iss. 8. P. 1524-1535. [In Russian].
Iterative refinement approach for improving convergence of the mixed precision linear solvers
B. I. Krasnopolsky
Institute of Mechanics, Lomonosov Moscow State University
Email: krasnopolsky@imec.msu.ru
DOI 10.24412/cl-35065-2021-1-01-74
The use of the lower precision floating point calculations is an evident way to speed up the solution of sys-
tems of linear algebraic equations. The widely used approach for iterative methods assumes the use of the
mixed precision calculations when the preconditioner is performed with the lower precision. In practice it can
provide 10-15 % calculations speedup. The more attractive way is the use of the lower precision for the whole
solver, which can reduce the calculation time by a factor of 1.6-1.8, but may affect the convergence rate.
The current talk discusses an alternative variant of introducing the mixed precision calculations, which
provides the double precision solution accuracy, but allows to perform most of the calculations in the single
precision [1]. The algorithm is based on the iterative refinement procedure and combines two nested iterative
methods: the simple outer method (e.g., Jacobi) performed in double precision and the more robust method
(e.g., BiCGStab + AMG preconditioner) performed in single precision. It is shown that the proper choice of the
inner solver stopping criteria is the key aspect of achieving the appropriate convergence rate, and the overall
convergence can be equal to the basic double precision method configuration, providing the decrease in the
calculation time by a factor of 1.6-1.7.
This work was supported by the Russian Science Foundation (grant 18-71-10075).
References
1. Krasnopolsky B., Medvedev A. Evaluating Performance of Mixed Precision Linear Solvers with Iterative Refinement
// Supercomputing Frontiers and Innovations. 2021 (accepted).
Numerical simulation of propellers rotation under cavitation conditions
O. L. Krutyakova, A. S. Kozelkov, V. V. Kurulin
FSUE �Russian Federal Nuclear Center � All-Russia Research Institute of Experimental Physics� Nizhny Novgorod
Region, Sarov
Email: kurulin@mail.ru
DOI 10.24412/cl-35065-2021-1-01-75
Cavitation influences the design of propellers considerably, so the research on their operation under cavi-
tation conditions is critical [1]. The work describes numerical simulation of cavitation processes when a model
VP1304 propeller is rotating. Volume of Fluid (VOF) method is used for numerical simulation, which is realized
in LOGOS software package. It allows numerical simulation of two-phase problems with free surface [2]. Cavi-
tation is accounted for when the method is supplemented with the account for the phase-to-phase mass ex-
change; cavitation models are used to compute its rates [3, 4]. The work shows a physical-mathematical mod-
el, briefly describes a numerical method used, as well as cavitation models; the models are compared after-
wards. Numerical simulation of the rotating propellers is demonstrated using the problems of flow-past of the
model VP1304 propeller under the conditions of developed cavitation.
References
1. A.N. Ivanov. Hydrodynamics of developed cavitation flows. Leningrad: Sudostroyeniye, 1980.
2. Kurulin V.V., Kozelkov A.S., Efremov V.R., Yatsevich S.V., Tarasova N.V. Application of VOF method to solve
complex problems with free surface // XXV All-Russia Workshop with international participation on jet, separated and
non-stationary flows. Saint-Petersburg, 2018. pp. 144-145.
3. Schnerr G. H., Sauer J. Physical and numerical modeling of unsteady cavitation dynamics // Proceedings of the
Fourth International Conference on Multiphase. Flow, New Orleans, USA, May 27 � June 1, 2001. P.1�12.
4. Zwart P.J., Gerber A.G., Belamri T. A Two-phase flow model for predicting cavitation dynamics // The Fifth
International Conference on Multiphase Flow. Yokohama, Japan. 2004.
Research on the accuracy of numerical simulation of acoustic perturbations in a fluid basing
on Navier � Stokes equations
O. L. Krutyakova, A. S. Kozelkov, V. V. Kurulin
FSUE �Russian Federal Nuclear Center � All-Russia Research Institute of Experimental Physics� Nizhny Novgorod
Region, Sarov
Email: kurulin@mail.ru
DOI 10.24412/cl-35065-2021-1-01-76
The work is devoted to the necessary space and time resolution when simulating the propagation of
acoustic perturbations in a fluid, analysis of the accuracy of the solution as a function of the parameters of the
