University
of Texas at Austin, Department of Civil, Architectural & Environmental
Engineering
The time-evolution
of the free surface in numerical models of the hydrostatic Navier-Stokes
equations is commonly accomplished with a 2nd-order Crank-Nicoloson
method. However, for unsteady solutions, a term that is formally 2nd-order
is neglected in prior formulations, which reduces the formal order
of accuracy of the method. More importantly, numerical tests show
that C-N method is, in practice, less than 2nd-order accurate when
the model time step is set so that the baroclinic CFL is greater than
unity.
Sponsor: Office of Naval Research,
Processes and Prediction Division
Program Officer: Dr. Theresa Paluszkiewicz
Award No. N00014-01-1-0574
Active Dates: 06/01/01 - 05/31/04
This is a secondary research issue discovered
under the primary study of internal waves. For the main project
page on this award <go
here>
Citation: Hodges, Ben R. (2003). "A second-order
correction for semi-implicit shallow water methods," in Electronic
Proceedings of the 16th ASCE Engineering Mechanics Conference, University
of Washington, Seattle, July 16-18, 2003.
Paper: Recently accepted at Journal
of Engineering Mechanics <
web abstract >
Citation: Hodges, B.R.
"Accuracy order of Crank-Nicolson Discretization for Hydrostatic
Free Surface Flow", to appear Journal of Engineering Mechanics,
Aug 2004.
Hydrostatic numerical model (CWR-ELCOM)
was set up to run a simple surface seiche (at left) with three different
ratios of seiche amplitude to domain depth (a/D) and for 3 different
grid dimensions both with and without the new second order correction.
Typical results (at
left) show that the the error is only 2nd order for small time steps.
Note that the CFL > 1 occurs for T/dt < 70, where all results
are less than 2nd-order accurate.
