TY - JOUR
T1 - An approach for choosing discretization schemes and grid size based on the convection-diffusion equation
AU - Zhou, Lin
AU - Gao, Zhenghong
AU - Gao, Yuan
N1 - Publisher Copyright:
© 2018, Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - A new approach for selecting proper discretization schemes and grid size is presented. This method is based on the convection-diffusion equation and can provide insight for the Navier-Stokes equation. The approach mainly addresses two aspects, i.e., the practical accuracy of diffusion term discretization and the behavior of high wavenumber disturbances. Two criteria are included in this approach. First, numerical diffusion should not affect the theoretical diffusion accuracy near the length scales of interest. This is achieved by requiring numerical diffusion to be smaller than the diffusion discretization error. Second, high wavenumber modes that are much smaller than the length scales of interest should not be amplified. These two criteria provide a range of suitable scheme combinations for convective flux and diffusive flux and an ideal interval for grid spacing. The effects of time discretization on these criteria are briefly discussed.
AB - A new approach for selecting proper discretization schemes and grid size is presented. This method is based on the convection-diffusion equation and can provide insight for the Navier-Stokes equation. The approach mainly addresses two aspects, i.e., the practical accuracy of diffusion term discretization and the behavior of high wavenumber disturbances. Two criteria are included in this approach. First, numerical diffusion should not affect the theoretical diffusion accuracy near the length scales of interest. This is achieved by requiring numerical diffusion to be smaller than the diffusion discretization error. Second, high wavenumber modes that are much smaller than the length scales of interest should not be amplified. These two criteria provide a range of suitable scheme combinations for convective flux and diffusive flux and an ideal interval for grid spacing. The effects of time discretization on these criteria are briefly discussed.
KW - cell Reynolds number
KW - convection-diffusion equation
KW - diffusion term accuracy
KW - high wavenumber mode
KW - scheme selection
UR - http://www.scopus.com/inward/record.url?scp=85045644003&partnerID=8YFLogxK
U2 - 10.1007/s10483-018-2341-9
DO - 10.1007/s10483-018-2341-9
M3 - 文章
AN - SCOPUS:85045644003
SN - 0253-4827
VL - 39
SP - 877
EP - 890
JO - Applied Mathematics and Mechanics (English Edition)
JF - Applied Mathematics and Mechanics (English Edition)
IS - 6
ER -