Skip to main content

Part of the book series: Springer Theses ((Springer Theses))

  • 804 Accesses

Abstract

Over the last several decades, computational fluid dynamics (CFD) methods are undergoing significant developments and have developed to be one of the most important tools in the research of fluid dynamics in additional to theoretical analysis and experiments. The CFD technique finds wide usage in different fields related to fluids, e.g., aerodynamics force and heat flow, configuration optimization, flow control strategies, and turbulence strength enhancement. Among these applications, the AIAA holds five drag prediction workshops [1] and the latest High Lift workshop [2], which aim at calculating the lift and drag force accurately using these methods. To make the CFD methods reliable, a lot of research has been conducted on the validation and verification of CFD methods.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. Levy DW, Laflin KR, Tinoco EN, et al (2013) Summary of data from the fifth AIAA CFD drag prediction workshop. AIAA Paper 2013-0046, 51st AIAA Aerospace Sciences Meeting, 7–10 Jan 2013. Grapevine, TX, United States

    Google Scholar 

  2. Slotnick JP, Hannon JA, Chaffin M (2011) Overview of the first AIAA CFD high lift prediction workshop (Invited). AIAA 2011-862, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 4–7Jan 2011. Orlando, Florida

    Google Scholar 

  3. Kroll N (2006) ADIGMA—a European project on the development of adaptive higher order variational methods for aerospace applations. European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2006

    Google Scholar 

  4. Kroll N (2009) ADIGMA—a European project on the development of adaptive higher-order variational methods for aerospace applications, 47th AIAA Aerospace Sciences Meeting. 2009-176

    Google Scholar 

  5. Industrialisation of High-Order Methods A Top-Down Approach (IDIHOM), FP7 reference number:265780, Duration: 2010.10.1 - 2013.09.30

    Google Scholar 

  6. Research Opportunities in Aeronautics (ROA) (2011) NASA Research Announcement (NRA):NNH10ZEA001N, August 26, 2011

    Google Scholar 

  7. Wang ZJ, Fidkowski K, Abgrall R, et al (2012) High-order CFD methods: current status and perspective. Int J Numer Meth Fluids: 1–42

    Google Scholar 

  8. Dumbser M, Schwartzkop T, Munz CD (2006) Arbitrary high order finite volume scheme for linear wave propagation. Book series notes on numerical fluid mechanics and multidisciplinary design, vol 91, pp 129–144

    Google Scholar 

  9. Dumbser M (2011) Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier-Stokes equations. Comput Fluids 39:60–76

    Article  MathSciNet  Google Scholar 

  10. Wang ZJ (2011) Adaptive high-order methods in computational fluid dynamics. World Scientific, New Jersey

    MATH  Google Scholar 

  11. Lele SK (1992) Compact finite difference scheme with spectral like resolution. J Comput Phys 103:16–42

    Article  MATH  MathSciNet  Google Scholar 

  12. Tam C, Webb JC (1993) Dispersion-relation-preserving finite difference schemes for computational acoustics. J Comput Phys 107:262–281

    Article  MATH  MathSciNet  Google Scholar 

  13. Shu CW Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA/CR-97-206253, ICASE, Report No. 97–65

    Google Scholar 

  14. Ren YX, Liu M, Zhang HX (2003) A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. J Comput Phys 192:365–386

    Article  MATH  MathSciNet  Google Scholar 

  15. Martin MP, Taylor EM, Wu M et al (2006) A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J Comput Phys 220:270–289

    Article  MATH  Google Scholar 

  16. Sun ZS, Ren YX, Larricq C et al (2011) A class of finite difference schemes with low dispersion and controllable dissipation for DNS of compressible turbulence. J Comp Phys 230:4616–4635

    Google Scholar 

  17. Cockburn B, Shu CW (2001) Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J Sci Comput 16:173–261

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang ZJ, Zhang L, Liu Y (2004) Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems. J Comput Phys 194:716–741

    Article  MATH  MathSciNet  Google Scholar 

  19. Liu Y, Vinokur M, Wang ZJ (2006) Spectral difference method for unstructured grids I: basis formulation. J Comput Phys 216:780–801

    Article  MATH  MathSciNet  Google Scholar 

  20. Wang ZJ, Gao H (2009) A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids. J Comput Phys 228:8161–8186

    Article  MATH  MathSciNet  Google Scholar 

  21. Huynh HT (2007) A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. 18th AIAA Computational Fluid Dynamics Conference, 25–28 June 2007. Miami, FL, AIAA2007-4079

    Google Scholar 

  22. Dumbser M, Zanotti O (2009) Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations. J Comput Phys 228:6991–7006

    Article  MATH  MathSciNet  Google Scholar 

  23. Barth TJ, Frederichson PO (1990) Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. 28th aerospace sciences meeting, 8–11 Jan. Reno, Nevada, AIAA90-0013

    Google Scholar 

  24. Delanaye M, Liu Y (1999) Quadratic reconstruction finite volume schemes on 3D arbitrary unstructured polyhedral grids. 14th Computational Fluid Dynamics Conference, AIAA99-3259

    Google Scholar 

  25. Abgrall R (1994) On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J Comput Phys 144:45–58

    Article  MathSciNet  Google Scholar 

  26. Abgrall R, Sonar T (1997) On the use of Mühlbach expansions in the recovery step of ENO methods. Numer Math 76:1–25

    Article  MATH  MathSciNet  Google Scholar 

  27. Friedrich O (1998) Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J Comput Phys 144:194–212

    Article  MathSciNet  Google Scholar 

  28. Van Abeele K, Lacor C (2007) An accuracy and stability study of the 2D spectral volume method. J Comput Phys 226:1007–1026

    Article  MATH  MathSciNet  Google Scholar 

  29. Van Abeele KV, Lacor C, Wang ZJ (2008) On the stability and accuracy of the spectral difference method. J Sci Comput 37:162–188

    Article  MATH  MathSciNet  Google Scholar 

  30. Balan A, May G, Schöberl J (2011) A stable spectral difference method for triangles. 49th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 4–7 Jan. Orando, Florida, AIAA2011-47

    Google Scholar 

  31. Cockburn B, Kanschat G, Perugia I et al (2011) Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. SIAM J Numer Anal 39:264–285

    Google Scholar 

  32. Collis SS, Ghayour K (2003) Discontinuous Galerkin methods for compressible DNS. In: Proceedings of FEDSM, ASME/JSME joint fluids engineering conference, 2003

    Google Scholar 

  33. Wei L, Pollard A (2011) Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method. Comput Fluids 44:85–100

    Article  MathSciNet  Google Scholar 

  34. Zhou Y, Wang ZJ (2010) Implicit large eddy simulation of transitional flow over a SD7003 wing using high-order spectral difference method. 40th fluid dynamics conference and exhibit, 28 June–1 July. Chicago, Illinois, AIAA2010-4442

    Google Scholar 

  35. Nogueira X et al (2010) Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme. J Comput App Math 234:2089–2097

    Article  MATH  MathSciNet  Google Scholar 

  36. Rao PP (2004) High order unstructured grid methods for computational aeroacoustics. Phd thesis, United States: the Pennsylvania State university

    Google Scholar 

  37. Dumbser M, Käser M (2007) Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J Comput Phys 221:693–723

    Article  MATH  MathSciNet  Google Scholar 

  38. Bassi F, Rebay S (1997) High-order accurate discontinuous finite element solution of the 2D Euler equations. J Comput Phys 138:251–285

    Article  MATH  MathSciNet  Google Scholar 

  39. Lübon C, Wagner S (2007) Three-dimensional discontinuous Galerkin codes to simulate viscous flow by spatial discretization of high order and curved elements on unstructured grids. New Res In Num Exp Fluid Mech 96:145–153

    Google Scholar 

  40. Ollivier-Gooch C, Altena MV (2002) A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation. J Comput Phys 181:729–752

    Article  MATH  Google Scholar 

  41. Krivodonova L, Berger M (2006) High-order accurate implementation of solid wall boundary conditions in curved geometries. J Comput Phys 211:492–512

    Article  MATH  MathSciNet  Google Scholar 

  42. Luo H, Baum JD, Löhner R (2008) On the computation of steady-state compressible flows using a discontinuous Galerkin method. Int J Numer Meth Eng 73:597–623

    Article  MATH  Google Scholar 

  43. Jiang GS, Shu CW (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126:202–228

    Article  MATH  MathSciNet  Google Scholar 

  44. Barth TJ, Jespersen D (1989) The design and application of upwind schemes on unstructured meshes. In: Proceedings of the 27th AIAA aerospace sciences meeting, Reno, NV, Paper AIAA 89–0366, 1989

    Google Scholar 

  45. Venkatakrishnan V (1995) Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J Comput Phys 118:120–130

    Article  MATH  Google Scholar 

  46. Park JS, Yoon SH, Kim C (2010) Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids. J Comput Phys 229:788–812

    Article  MATH  MathSciNet  Google Scholar 

  47. Hu C, Shu CW (1999) Weighted essentially non-oscillatory schemes on triangular meshes. J Comput Phys 150:97–127

    Article  MATH  MathSciNet  Google Scholar 

  48. Zhu J, Qiu J (2009) Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method III: unstructured meshes. J Sci Comput 39:293–321

    Article  MATH  MathSciNet  Google Scholar 

  49. Krivodonova L (2007) Limiters for high-order discontinuous Galerkin methods. J Comput Phys 226:879–896

    Article  MATH  MathSciNet  Google Scholar 

  50. Xu Z, Liu Y, Shu CW (2009) Hierarchical reconstructin for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells. J Comput Phys 228:2194–2212

    Article  MATH  MathSciNet  Google Scholar 

  51. Xu Z, Liu Y, Shu CW (2011) Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws. J Comput Phys 230:6843–6865

    Article  MATH  MathSciNet  Google Scholar 

  52. Park JS, Kim C (2011) Higher-order discontinuous Galerkin-MLP methods on triangular and tetrahedral grids. In: Proceedings of AIAA 2011–3059, 20th AIAA computational fluid dynamics conference, 27–30 June 2011, Honolulu, Hawaii

    Google Scholar 

  53. Burbeau A, Sagaut P, Bruneau CH (2011) A problem-independent limiter for high-order RungeCKutta discontinuous Galerkin methods. J Comput Phys 169:111C150

    Google Scholar 

  54. Krivodonova L et al (2004) Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws. Appl Num Math 48:323–338

    Google Scholar 

  55. Dumbser M, Käser M, Toro EF (2007) An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes V: local time stepping and p-adaptivity. Geophys J Int 171:695C717

    Google Scholar 

  56. Kanevsky A et al (2007) Application of implicit-explicit high-order Runge-Kutta methods to discontinuous Galerkin schemes. J Comput Phys 225:1753–1781

    Article  MATH  MathSciNet  Google Scholar 

  57. Dumbser M, Käser M, Titarev VA et al (2007) Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 226:204–243

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wanai Li .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Li, W. (2014). Introduction. In: Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43432-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43432-1_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43431-4

  • Online ISBN: 978-3-662-43432-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics