TY - JOUR
T1 - Extension of Kleiser and Schumann's influence-matrix method for generalized velocity boundary conditions
AU - Liu, X.
N1 - Funding Information:
This work was supported by the startup fund to Xiaofeng Liu from the University of Texas at San Antonio, USA . This work was also partially supported by the National Center for Supercomputing Applications under project TG-CTS100063 and utilized the SGI Altix system Cobalt.
PY - 2011/9/10
Y1 - 2011/9/10
N2 - In 1980, Kleiser and Schumann introduced a novel influence-matrix method to treat the incompressibility and no-slip boundary conditions when solving the Navier-Stokes equations. They also outlined the related " tau" error correction technique which is essential for the high accuracy direct numerical simulation (DNS) of turbulent flows. However, their method is not valid for Robin type velocity boundary conditions (i.e., B(u) = αu+. βu' - γ= 0). In this note, a new influence-matrix method is introduced where the boundary condition and " tau" correction are enforced in one step using an extended influence matrix. The new method is simple and easy to be implemented. It broadens the applicability of the Kleiser and Schumann method. Examples with the new method show excellent agreement with data in the literature and the velocity field is divergence free up to machine precision.
AB - In 1980, Kleiser and Schumann introduced a novel influence-matrix method to treat the incompressibility and no-slip boundary conditions when solving the Navier-Stokes equations. They also outlined the related " tau" error correction technique which is essential for the high accuracy direct numerical simulation (DNS) of turbulent flows. However, their method is not valid for Robin type velocity boundary conditions (i.e., B(u) = αu+. βu' - γ= 0). In this note, a new influence-matrix method is introduced where the boundary condition and " tau" correction are enforced in one step using an extended influence matrix. The new method is simple and easy to be implemented. It broadens the applicability of the Kleiser and Schumann method. Examples with the new method show excellent agreement with data in the literature and the velocity field is divergence free up to machine precision.
UR - http://www.scopus.com/inward/record.url?scp=80052689511&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052689511&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2011.07.016
DO - 10.1016/j.jcp.2011.07.016
M3 - Article
AN - SCOPUS:80052689511
SN - 0021-9991
VL - 230
SP - 7911
EP - 7916
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 22
ER -