TY - JOUR
T1 - A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
AU - Ben-Artzi, Matania
AU - Croisille, Jean Pierre
AU - Fishelov, Dalia
AU - Trachtenberg, Shlomo
PY - 2005/5/20
Y1 - 2005/5/20
N2 - A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity-streamfunction evolution equation by the Laplacian of the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to be invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed. A number of numerical experiments are presented, including driven and double driven cavities, where the Reynolds numbers are sufficiently large, leading to symmetry breaking of asymptotic solutions.
AB - A pure-streamfunction formulation is introduced for the numerical simulation of the two-dimensional incompressible Navier-Stokes equations. The idea is to replace the vorticity in the vorticity-streamfunction evolution equation by the Laplacian of the streamfunction. The resulting formulation includes the streamfunction only, thus no inter-function relations need to be invoked. A compact numerical scheme, which interpolates streamfunction values as well as its first order derivatives, is presented and analyzed. A number of numerical experiments are presented, including driven and double driven cavities, where the Reynolds numbers are sufficiently large, leading to symmetry breaking of asymptotic solutions.
KW - Asymptotic behavior
KW - Compact schemes
KW - Driven cavity
KW - Navier-Stokes equations
KW - Numerical algorithm
KW - Streamfunction formulation
KW - Symmetry breaking
KW - Vorticity
UR - http://www.scopus.com/inward/record.url?scp=17144404238&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2004.11.024
DO - 10.1016/j.jcp.2004.11.024
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AN - SCOPUS:17144404238
SN - 0021-9991
VL - 205
SP - 640
EP - 664
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -