%0 Report %1 goodrich1989bifurcation %A Goodrich, John W. %A Gustafson, Karl %A Halasi, Kadosa %D 1989 %K 76e09-stability-and-instability-of-nonparallel-flows 76e15-absolute-and-convective-instability-and-stability 76m25-other-numerical-methods-in-fluid-mechanics 76r05-forced-convection 80a20-heat-and-mass-transfer %N 102334 %T Hopf bifurcation in the driven cavity %U https://ntrs.nasa.gov/citations/19900002653 %X Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.

@techreport{goodrich1989bifurcation, abstract = {Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.}, added-at = {2021-01-18T05:42:20.000+0100}, author = {Goodrich, John W. and Gustafson, Karl and Halasi, Kadosa}, biburl = {https://www.bibsonomy.org/bibtex/2d265aac5868800926dfec0b2b54b63ab/gdmcbain}, institution = {NASA}, interhash = {415e29809794df8912c837985b797e7f}, intrahash = {d265aac5868800926dfec0b2b54b63ab}, keywords = {76e09-stability-and-instability-of-nonparallel-flows 76e15-absolute-and-convective-instability-and-stability 76m25-other-numerical-methods-in-fluid-mechanics 76r05-forced-convection 80a20-heat-and-mass-transfer}, number = 102334, timestamp = {2021-01-18T05:44:31.000+0100}, title = {Hopf bifurcation in the driven cavity}, type = {Technical Memorandum}, url = {https://ntrs.nasa.gov/citations/19900002653}, year = 1989 }