%0 Journal Article %1 goodrich1990bifurcation %A Goodrich, John W %A Gustafson, Karl %A Halasi, Kadosa %D 1990 %J Journal of Computational Physics %K 76e09-stability-and-instability-of-nonparallel-flows %N 1 %P 219 - 261 %R https://doi.org/10.1016/0021-9991(90)90204-E %T Hopf bifurcation in the driven cavity %U http://www.sciencedirect.com/science/article/pii/002199919090204E %V 90 %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 stream-function 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 have been reached. A discussion is included about the indicators that are used to show that an asymptotic state has been reached and to show that the asymptotic state is indeed periodic.

@article{goodrich1990bifurcation, 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 stream-function 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 have been reached. A discussion is included about the indicators that are used to show that an asymptotic state has been reached and to show that the asymptotic state is indeed periodic.}, added-at = {2021-01-18T05:43:38.000+0100}, author = {Goodrich, John W and Gustafson, Karl and Halasi, Kadosa}, biburl = {https://www.bibsonomy.org/bibtex/2b11878530d46ff478d19e666b6dd6172/gdmcbain}, doi = {https://doi.org/10.1016/0021-9991(90)90204-E}, interhash = {e5f700e1b5dbdf6f8da0e872ba7b6f3a}, intrahash = {b11878530d46ff478d19e666b6dd6172}, issn = {0021-9991}, journal = {Journal of Computational Physics}, keywords = {76e09-stability-and-instability-of-nonparallel-flows}, number = 1, pages = {219 - 261}, timestamp = {2021-01-18T05:43:38.000+0100}, title = {Hopf bifurcation in the driven cavity}, url = {http://www.sciencedirect.com/science/article/pii/002199919090204E}, volume = 90, year = 1990 }