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Article information
2019 , Volume 24, ¹ 1, p.106-119
Tyatyushkina E.S., Kozelkov A.S., Kurkin A.A., Kurulin V.V., Efremov V.R., Utkin D.A.
Evaluation of numerical diffusion of the finite volume method when modelling surface waves
The application of numerical simulation methods based on the solution of the full three-dimensional Navier-Stokes equations for modelling of wave propagation on the water surface requires the construction of a grid model containing countable nodes throughout the entire volume of water medium. Insufficient grid resolution leads to insufficient detailing of the fields of velocity and pressure, as well as volume fraction of the liquid, which increases the numerical diffusion of the method and, ultimately, leads to an underestimation of oscillation amplitudes of the medium. A large time step also results in a “blurring” of the solution and significantly reduces its stability, especially when using the schemes which compress the front of the media interface. This paper presents the results of an assessment of acceptable grid sizes and time steps expressed in dimensionless parameters with respect to the wave parameters necessary to ensure accuracy of the solution sufficient for geophysical applications. The estimate is given for the method of calculating three-dimensional multiphase flows with a free surface based on solving the Navier-Stokes equations in a one-velocity approximation based on a completely implicit connection between velocity and pressure using the finite volume method. The finite volume method for the numerical solution of the Navier-Stokes equations is implemented for use on arbitrary unstructured grids. The methodology for estimation of numerical diffusion of the calculation method is proposed. This estimation is expressed as a percentage of the wave amplitude decrease at the distance equal to the one wavelength. In turn the methodology is based on the parameters entered to estimate the acceptable grid sizes and time step for the calculation method. Based on the described methodology, the results of the estimation of the grid resolution in the horizontal and vertical directions, the estimation of the time step, and the evaluation of the influence of the discretization scheme of the convective term are presented.
[full text] [link to elibrary.ru]
Keywords: surface waves, volume of fluid, method of finite volume, difference scheme, grid resolution
doi: 10.25743/ICT.2019.24.1.008
Author(s):
Tyatyushkina Elena Sergeevna
Position: Junior Research Scientist
Office: Russian Federal Nuclear Center All-Russian research institute of experimental physics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
Address: 607189, Russia, Sarov, Mira ave., 37
Phone Office: (83130) 27372
E-mail: leno4ka-07@mail.ru
Kozelkov Andrey Sergeevich
Dr.
Position: Professor
Office: Russian Federal Nuclear Center, All-Russian Research Institute OF Experimental Physics
Address: 607189, Russia, Sarov, Mira ave., 37
Phone Office: (83130) 2 73 43
E-mail: askozelkov@mail.ru
SPIN-code: 6563-1107Kurkin Andrey Aleksandrovich
Dr. , Professor
Position: General Scientist
Office: Nizhny Novgorod State Technical University n.a. R.E. Alekseev
Address: 603950, Russia, Nizhny Novgorod, 24 Minin str.
Phone Office: (831) 436 04 89
E-mail: aakurkin@gmail.com
Kurulin Vadim Viktorovich
PhD.
Position: Head of department
Office: Russian Federal Nuclear Center All-Russian research institute of experimental physics
Address: 607189, Russia, Sarov, Mira ave., 37
Phone Office: (83130) 27567
E-mail: kurulin@mail.ru
SPIN-code: 1984-4399Efremov Valentin Robertovich
Position: Councilor
Office: Joint-Stock Company KBP n.a. Academician A. Shipunov
Address: 300001, Russia, Tula, 59 Shcheglovskaya Zaseka Str.
Phone Office: (4872)25-26-27
E-mail: valentin_e@mail.ru
Utkin Dmitriy Alexandrovich
Office: Russian Federal Nuclear Center All-Russian research institute of experimental physics
Address: 607189, Russia, Sarov, Mira ave., 37
Phone Office: (83130) 27144
E-mail: dimitryavich@yandex.ru
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Bibliography link:
Tyatyushkina E.S., Kozelkov A.S., Kurkin A.A., Kurulin V.V., Efremov V.R., Utkin D.A. Evaluation of numerical diffusion of the finite volume method when modelling surface waves // Computational technologies. 2019. V. 24. ¹ 1. P. 106-119
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