Skip to main content
SpringerLink
Log in

Applications to Laminar Flows in Nonlinear Fluid Mechanics

  • Chapter
  • First Online:
Wavelet Numerical Method and Its Applications in Nonlinear Problems

Part of the book series: Engineering Applications of Computational Methods ((EACM,volume 6))

  • 568 Accesses

Abstract

The previous chapter has discussed the closed wavelet-based method to solve the nonlinear problems of solid mechanics.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bateman H (1915) Some recent researches on the motion of fluids. Mon Weather Rev 43:163–170

    Article  Google Scholar 

  2. Burgers JM (1995) Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion. Springer, Dordrecht, pp 281–334

    Google Scholar 

  3. Burgers JM (1948) A mathematical model illustrating the theory of turbulence. Adv Appl Mech 1:171–199

    Article  MathSciNet  Google Scholar 

  4. Lai LL, Cheng RJ, Li ZP, Ge HX (2013) The KdV–Burgers equation in a modified speed gradient continuum model. Chin Phys B 22:060511

    Article  Google Scholar 

  5. Zhang XH, Ouyang J, Zhang L (2009) Element-free characteristic Galerkin method for Burgers’ equation. Eng Anal Bound Elem 33:356–362

    Article  MathSciNet  Google Scholar 

  6. Mittal RC, Jiwari R (2012) Differential quadrature method for numerical solution of coupled viscous Burgers’ equations. Int J Comput Methods Eng Sci Mech 13:88–92

    Article  MathSciNet  Google Scholar 

  7. Liu XJ, Wang JZ, Zhou YH (2016) A space-time fully decoupled wavelet Galerkin method for solving two-dimensional Burgers’ equations. Comput Math Appl 72:2908–2919

    Article  MathSciNet  Google Scholar 

  8. Kutluay S, Esen A, Dag I (2004) Numerical solutions of the Burgers’ equation by the least-squares quadratic B-spline finite element method. J Comput Appl Math 167:21–33

    Article  MathSciNet  Google Scholar 

  9. Hassanien IA, Salama AA, Hosham HA (2005) Fourth-order finite difference method for solving Burgers’ equation. Appl Math Comput 170:781–800

    MathSciNet  MATH  Google Scholar 

  10. Saka B, Dag I (2007) Quartic B-spline collocation method to the numerical solutions of the Burgers’ equation. Chaos Soliton and Fractals 32:1125–1137

    Article  MathSciNet  Google Scholar 

  11. Kakuda K, Tosaka N (1990) The generalized boundary element approach to Burgers’ equation. Int J Numer Methods Eng 29:245–261

    Article  Google Scholar 

  12. Evans DJ, Abdullah AR (1984) The group explicit method for the solution of Burgers’ equation. Computing 32:239–253

    Article  MathSciNet  Google Scholar 

  13. Gardner LRT, Gardner GA, Dogan A (1997) A Petrov-Galerkin finite element scheme for Burgers’ equation. Arab J Sci Eng 22:99–109

    MathSciNet  MATH  Google Scholar 

  14. Xie H, Li D (2013) A meshless method for Burgers’ equation using MQ-RBF and high-order temporal approximation. Appl Math Model 37:9215–9222

    Article  MathSciNet  Google Scholar 

  15. Jiwari R, Mittal RC, Sharma KK (2013) A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers’ equation. Appl Math Comput 219:6680–6691

    MathSciNet  MATH  Google Scholar 

  16. Gao Y, Le LH, Shi BC (2013) Numerical solution of Burgers’ equation by lattice Boltzmann method. Appl Math Comput 219:7685–7692

    MathSciNet  MATH  Google Scholar 

  17. Deville MO, Fischer PF, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge University Press, Cambridge

    Book  Google Scholar 

  18. Liu XJ, Zhou YH, Zhang L, Wang JZ (2014) Wavelet solutions of Burgers’ equation with high Reynolds numbers. Sci China Technol Sci 57:1285–1292

    Article  Google Scholar 

  19. Hon YC, Mao XZ (1998) An efficient numerical scheme for Burgers’ equation. Appl Math Comput 95:37–50

    MathSciNet  MATH  Google Scholar 

  20. Mittal RC, Jain RK (2012) Numerical solutions of nonlinear Burgers’ equation with modified cubic B-splines collocation method. Appl Math Comput 218:7839–7855

    MathSciNet  MATH  Google Scholar 

  21. Chen R, Wu Z (2006) Applying multiquadric quasi-interpolation to solve Burgers’ equation. Appl Math Comput 172:472–484

    MathSciNet  MATH  Google Scholar 

  22. Zhu CG, Wang RH (2009) Numerical solution of Burgers’ equation by cubic B-spline quasi-interpolation. Appl Math Comput 208:260–272

    MathSciNet  MATH  Google Scholar 

  23. Liu XJ, Wang JZ, Zhou YH (2013) A wavelet method for solving coupled viscous Burgers’ equations. In: AIP conference proceedings, vol 1558, pp 935–937

    Google Scholar 

  24. Hammad DA, El-Azab MS (2015) 2N order compact finite difference scheme with collocation method for solving the generalized Burger’s–Huxley and Burgers–Fisher equations. Appl Math Comput 258:296–311

    Google Scholar 

  25. Young DL, Fan CM, Hu SP, Atluri SN (2008) The Eulerian-Lagrangian method of fundamental solutions for two-dimensional unsteady Burgers’ equations. Eng Anal Bound Elem 32:395–412

    Article  Google Scholar 

  26. Duan YL, Liu RX (2007) Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation. J Comput Appl Math 206:432–439

    Article  MathSciNet  Google Scholar 

  27. Islam S, Aziz I, Al-Fhaid AS, Shah A (2013) A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets. Appl Math Model 37:9455–9481

    Article  MathSciNet  Google Scholar 

  28. Liao W (2010) A fourth-order finite-difference method for solving the system of two-dimensional Burgers’ equations. Int J Numer Methods Fluids 64:565–590

    Article  MathSciNet  Google Scholar 

  29. Zhang J, Yan G (2008) Lattice Boltzmann method for one and two-dimensional Burgers equation. Phys A 387:4771–4786

    Article  MathSciNet  Google Scholar 

  30. Lobovsky L, Kren J (2007) Smoothed particle hydrodynamics modelling of fluids and solids. Appl Comput Mech 1:521–530

    Google Scholar 

  31. Kundu PK, Cohen IM, Dowling DR (2012) Fluid mechanics, 5th edn. Elsevier, New York

    Google Scholar 

  32. Karniadakis GE, Israeli M, Orszag SA (1991) High-order splitting methods for the incompressible Navier-Stokes equations. J Comput Phys 97:414–443

    Article  MathSciNet  Google Scholar 

  33. Guo ZL, Zheng CG, Shi BC (2002) Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin Phys 11:366–374

    Article  Google Scholar 

  34. Schneider K, Kevlahan NKR, Farge M (1997) Comparison of an adaptive wavelet method and nonlinearly filtered pseudospectral methods for two-dimensional turbulence. Theoret Comput Fluid Dyn 9:191–206

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu, China

    Prof. You-He Zhou

Authors
  1. Prof. You-He Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to You-He Zhou .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhou, YH. (2021). Applications to Laminar Flows in Nonlinear Fluid Mechanics. In: Wavelet Numerical Method and Its Applications in Nonlinear Problems. Engineering Applications of Computational Methods, vol 6. Springer, Singapore. https://doi.org/10.1007/978-981-33-6643-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-981-33-6643-5_10

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-33-6642-8

  • Online ISBN: 978-981-33-6643-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation