Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Applied Mathematics and Mechanics in Aerospace Industry Read chapter Read first chapter

2021 | OriginalPaper | Chapter

4. Mathematical Modeling of Wave Motions of Fluids

Authors : Valentin A. Gushchin, Vasilii G. Kondakov, Irina A. Smirnova

Published in: Applied Mathematics and Computational Mechanics for Smart Applications

Publisher: Springer Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The study of wave movements of liquids is of interest both theoretically and practically. This can include flows with a free surface and flows with internal waves. For correct mathematical modeling of such flows, the finite-difference schemes of methods must have such properties as follows: high order of approximation, minimal scheme dissipation and dispersion, performance in a wide range of the Reynolds and the Froude numbers, and that is especially important the property of monotonicity. This chapter presents two approaches: splitting method for incompressible fluid flow (SMIF) method and compact accurately boundary adjusting high-resolution technique (CABARET) method, of course, whose finite-difference schemes have the properties listed above. A number of test tasks are considered and compared with theoretical, experimental data and calculations of other authors.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Numerical Simulation of Flow Structure Near Descent Module in Mars Atmosphere
next chapter Numerical Simulation of Taylor Vortex Flows Under the Periodicity Conditions
Literature
1.
Belotserkovskii, O., Gushchin, V., Shchennikov, V.: Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid. USSR Comput. Math. Math. Phys. 15(1), 190–200 (1975)CrossRef
2.
Gushchin, V.: Family of quasi-monotonic finite-difference schemes of the second-order of approximation. Math. Models Comput. Simul. 8, 487–496 (2016)MathSciNetCrossRef
3.
Goloviznin, V., Samarskii, A.: Some characteristics of finite difference scheme “CABARET”. Math. Mod. 10(1), 101–116 (1998) (in Russian)
4.
Goloviznin, V., Samarskii, A.: Finite difference approximation of convective transport equation with space splitting time derivative. Math. Mod. 10(1), 86–100 (1998) (in Russian)
5.
Goloviznin, V., Karabasov, S., Kondakov, V.: Generalization of the CABARET scheme to two-dimensional orthogonal computational grids. Math. Models Comput. Simul. 6(1), 56–79 (2014)CrossRef
6.
Glotov, V., Goloviznin, V.: CABARET scheme in velocity–pressure formulation for two-dimensional incompressible fluids. Comput. Math. Math. Phys. 53(6), 721–735 (2013)MathSciNetCrossRef
7.
Gushchin, V., Matyushin, P.: Method SMIF for incompressible fluid flows modeling. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) Numerical Analysis and Its Applications. NAA 2012. LNCS, vol. 8236, pp. 311–318. Springer, Berlin, Heidelberg (2013)
8.
Glotov, V., Goloviznin, V., Kanaev, A., Kondakov, V., Kiselev, A.: CABARET scheme for modelling the stratification erosion in gas mixtures in hydrogen mitigation experiments for reactor safety. J. Phys.: Conf. Ser. 1392(1), 012039.1–012039.7 (2019)
9.
Belotserkovskii, O., Gushchin, V., Kon’shin, V.: The splitting method for investigating flows of a stratified liquid with a free surface. USSR Comput. Math. Math. Phys. 27(2), 181–191 (1987)CrossRef
10.
Gushchin, V., Kondakov, V.: On the Cabaret scheme for incompressible fluid flow problems with a free surface. Math. Models Comput. Simul. 11(4), 499–508 (2019)MathSciNetCrossRef
11.
Gushchin, V.: The splitting method for problems of the dynamics of an inhomogeneous viscous incompressible fluid. USSR Comput. Math. Math. Phys. 21(4), 190–204 (1981)MathSciNetCrossRef
12.
Gushchin, V., Kondakov, V.: Solution of the problems of nonhomogeneous in-compressible fluid dynamics by the CABARET method. AIP Conf. Proc. 2164(1), 120007.1–120007.8 (2019)
13.
Gushchin, V., Kondakov, V.: Mathematical modeling of free-surface flows using multiprocessor computing systems. J. Phys.: Conf. Ser. 1392(1), 012042.1–012042.6 (2019)
14.
Gushchin, V., Smirnova, I.: On one approach for mathematical modeling of the mixed zones dynamics in a stratified fluid. AIP Conf. Proc. 2172(1), 070017.1–070017.7 (2019)
15.
Gushchin, V., Smirnova, I.: The splitting scheme for mathematical modeling of the mixed region dynamics in a stratified fluid. In: Jain, L.C., Favorskaya, M.N., Nikitin, I.S., Reviznikov, D.L. (eds.) Advances in Theory and Practice of Computational Mechanics. Smart Innovation, Systems and Technologies, vol. 173, pp. 11–21. Springer, Singapore (2020)
16.
Barenblatt, G.: Dynamics of turbulent spots and intrusions in stably stratified fluid. Izv. Acad. Sci. USSR. Phys. Atmos. Ocean 14(2), 195–206 (1978) (in Russian)
17.
Gushchin, V., Mitkin, V., Rozhdestvenskaya, T., Chashechkin, Yu.D.: Numerical and experimental study of the fine structure of a stratified fluid flow over a circular cylinder. J. Appl. Mech. Tech. Phys. 48, 34–43 (2007)CrossRef
18.
Gushchin, V., Matyushin, P.: Simulation and study of stratified flows around finite bodies. Comput. Math. Math. Phys. 56, 1034–1047 (2016)MathSciNetCrossRef
19.
Gushchin, V., Kopysov, A.: The dynamics of a spherical mixing zone in a stratified fluid and its acoustic radiation. Comput. Math. Math. Phys. 31(6), 51–60 (1991)MathSciNetMATH
20.
Gushchin, V., Smirnova, I.: Mathematical modeling of spot dynamics in a stratified medium. Comput. Math. Math. Phys. 60(5), 879–894 (2020)MathSciNetCrossRef
21.
Gushchin, V., Kondakov, V.: One approach of solving tasks in the presence of free surface using a multiprocessor computing systems. In: Lirkov, I., Margenov, S. (eds.) Large-Scale Scientific Computing. LSSC 2019. LNCS, vol. 11958, pp. 324–331. Springer, Cham (2020)
22.
Kuznetsov, Yu., Rossi, T.: Fast direct method for solving algebraic systems with separable symmetric band matrices. East-West J. Numer. Math. 4(1), 53–68 (1996)MathSciNetMATH
23.
Wessel, W.: Numerical study of the collapse of a perturbation in an infinite density stratified fluid. Phys. Fluids 12(12), 170–176 (1969)CrossRef
24.
Zatsepin, G., Fedorov, K.N., Voropaev, S.I., Pavlov, A.M.: Experimental research of collapse mixed spot in stratified fluid. Izv. Acad. Sci. USSR. Phys. Atmos. Ocean 14(2), 234–237 (1978) (in Russian)
Metadata
Title
Mathematical Modeling of Wave Motions of Fluids
Authors
Valentin A. Gushchin
Vasilii G. Kondakov
Irina A. Smirnova
Copyright Year
2021
Publisher
Springer Singapore
Book
Applied Mathematics and Computational Mechanics for Smart Applications

Print ISBN: 978-981-334-825-7

Electronic ISBN: 978-981-334-826-4

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-33-4826-4_4

Premium Partner

    Image Credits