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Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil

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Abstract

The preconditioning technique can address the stiffness of a low Mach number flow, while its stability is poor. Based on the conventional preconditioning method of Roe's scheme, a low-diffusion scheme is proposed. An adjustable parameter is introduced to control numerical dissipation, especially over the dissipation in the boundary layer and extremely in a low speed region. Numerical simulations of the low Mach number and low Reynolds number flows past a cylinder and the low Mach number and high Reynolds number flows past NACA0012 and S809 airfoils are performed to validate the new scheme. Results of the three tests well agree with experimental data, showing the applicability of the proposed scheme to low Mach number flow simulations.

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Abbreviations

q :

primitive variable

ρ :

density

u :

velocityinthex-direction

υ :

velocityinthe y-direction

T :

temperature

ξ, η :

computational coordinates

F :

inviscid flux in the ξ-direction

G :

inviscid flux in the η-direction

F ν :

viscid flux in the ξ-direction

G ν :

viscid flux in the η-direction

D :

cylinder diameter

Re :

Reynolds number

C P :

pressure coefficient

Γ:

preconditioning matrix

ɛ :

preconditioning parameter

H :

total enthalpy

c p :

specific heat at constant pressure

R :

gas constant

λ :

eigenvalue

\(\hat R\) :

right eigenvector matrix

α :

adjustable parameter

Ma :

localMachnumber

Ma f :

free stream Mach number

Ma l :

local maximum Mach number of adjacent cells

L :

cylinder vortex size

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Author information

Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, P. R. China

    Qian Xiang  (相 倩), Song-ping Wu  (吴颂平), Chun-hian Lee  (李椿萱) & Ning cao  (曹 宁)

  2. National Laboratory for Computational Fluid Dynamics, Beihang University, Beijing, 100191, P. R. China

    Qian Xiang  (相 倩), Song-ping Wu  (吴颂平), Chun-hian Lee  (李椿萱) & Ning cao  (曹 宁)

  3. Ministry of Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing, 100191, P. R. China

    Qian Xiang  (相 倩), Song-ping Wu  (吴颂平), Chun-hian Lee  (李椿萱) & Ning cao  (曹 宁)

Authors
  1. Qian Xiang  (相 倩)
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  2. Song-ping Wu  (吴颂平)
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  3. Chun-hian Lee  (李椿萱)
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  4. Ning cao  (曹 宁)
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Corresponding author

Correspondence to Qian Xiang  (相 倩).

Additional information

Communicated by Wen-rui HU

Project supportedbytheNationalBasicResearchProgramofChina(973Program) (No. 2007CB714600)

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Xiang, Q., Wu, Sp., Lee, Ch. et al. Low-diffusion preconditioning scheme for numerical simulation of low-speed flows past airfoil. Appl. Math. Mech.-Engl. Ed. 32, 613–620 (2011). https://doi.org/10.1007/s10483-011-1443-8

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  • DOI: https://doi.org/10.1007/s10483-011-1443-8

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