Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

An Asymptotic Approach to Compare Coupling Mechanisms for Different Partial Differential Equations

  • Conference paper
  • First Online:
Domain Decomposition Methods in Science and Engineering XX

Abstract

In many applications the viscous terms become only important in parts of the computational domain. A typical example is the flow of air around the wing of an airplane. It can then be desirable to use an expensive viscous model only where the viscosity is essential for the solution and an inviscid one elsewhere. This leads to the interesting problem of coupling partial differential equations of different types.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

Bibliography

  1. Y. Achdou and O. Pironneau. The χ-method for the Navier-Stokes equations. IMA J. Numer. Anal., 13(4):537–558, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Agoshkov, P. Gervasio, and A. Quarteroni. Optimal control in heterogeneous domain decomposition methods for advection-diffusion equations. Mediterr. J. Math., 3(2):147–176, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  3. F. Brezzi, C. Canuto, and A. Russo. A self-adaptive formulation for the Euler/Navier-Stokes coupling. Comput. Methods Appl. Mech. Engrg., 73(3):317–330, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. A. Coclici, G. Moroşanu, and W. L. Wendland. The coupling of hyperbolic and elliptic boundary value problems with variable coefficients. Math. Methods Appl. Sci., 23(5):401–440, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  5. Q. V. Dinh, R. Glowinski, J. Périaux, and G. Terrasson. On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition. In First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), pages 350–369. SIAM, Philadelphia, PA, 1988.

    Google Scholar 

  6. M. Discacciati, Gervasio P., and A. Quarteroni. Heterogeneous mathematical models in fluid dynamics and associated solution algorithms. Tech. Report MOX 04/2010, 2010.

    Google Scholar 

  7. M. J. Gander, L. Halpern, C. Japhet, and V. Martin. Viscous problems with inviscid approximations in subregions: a new approach based on operator factorization. In CANUM 2008, volume 27 of ESAIM Proc., pages 272–288. EDP Sci., Les Ulis, 2009.

    Google Scholar 

  8. M. J. Gander, L. Halpern, and V. Martin. How close to the fully viscous solution can one get with inviscid approximations in subregions ? In Domain Decomposition Methods in Science and Engineering XIX, volume 78 of Lect. Notes Comput. Sci. Eng., pages 237–244. Springer, 2011.

    Google Scholar 

  9. F. Gastaldi and A. Quarteroni. On the coupling of hyperbolic and parabolic systems: analytical and numerical approach. Appl. Numer. Math., 6(1–2):3–31, 1989/90. Spectral multi-domain methods (Paris, 1988).

    Google Scholar 

  10. P. Gervasio, J.-L. Lions, and A. Quarteroni. Heterogeneous coupling by virtual control methods. Numer. Math., 90(2):241–264, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  11. C.-H. Lai, A. M. Cuffe, and K. A. Pericleous. A defect equation approach for the coupling of subdomains in domain decomposition methods. Comput. Math. Appl., 35(6):81–94, 1998.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin J. Gander .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gander, M.J., Martin, V. (2013). An Asymptotic Approach to Compare Coupling Mechanisms for Different Partial Differential Equations. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_51

Download citation

Publish with us

Policies and ethics