TY - JOUR
T1 - A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows
AU - Li, Ming
AU - Tang, Tao
N1 - Funding Information:
We would like to thank the referees for careful reading for the manuscript and for helpful suggestions. This research was partially supported by NSERC Canada under grant number OGP0105545 and by Hong Kong Baptist University under grant numbers FRG 98-99 II-14 and 15.
PY - 2001/3
Y1 - 2001/3
N2 - In this paper, we extend a previous work on a compact scheme for the steady Navier-Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137-1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier-Stokes equations are discretized in space within a 3 x 3 stencil such that a fourth order accuracy is achieved. The time derivatives are discretized in such a way as to maintain the compactness of the stencil. We explore several known time-stepping approaches including second-order BDF method, fourth-order BDF method and the Crank-Nicolson method. Numerical solutions are obtained for the driven cavity problem and are compared with solutions available in the literature. For large values of the Reynolds number, it is found that high-order time discretizations outperform the low-order ones.
AB - In this paper, we extend a previous work on a compact scheme for the steady Navier-Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137-1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier-Stokes equations are discretized in space within a 3 x 3 stencil such that a fourth order accuracy is achieved. The time derivatives are discretized in such a way as to maintain the compactness of the stencil. We explore several known time-stepping approaches including second-order BDF method, fourth-order BDF method and the Crank-Nicolson method. Numerical solutions are obtained for the driven cavity problem and are compared with solutions available in the literature. For large values of the Reynolds number, it is found that high-order time discretizations outperform the low-order ones.
KW - Navier–Stokes equations
KW - streamfunction
KW - vorticity
KW - compact scheme
UR - http://www.scopus.com/inward/record.url?scp=0042696191&partnerID=8YFLogxK
U2 - 10.1023/A:1011146429794
DO - 10.1023/A:1011146429794
M3 - Journal article
AN - SCOPUS:0042696191
SN - 0885-7474
VL - 16
SP - 29
EP - 45
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -