![[Back]](/images/prevpage.gif)
![[Index]](/images/index.gif)
![[Help]](/images/help.gif)
![[MSI]](/images/msi.gif)
![[ANU Online]](/images/online.gif)
Research Report MRR00-026
Explicit Schemes for Dam-Break Simulations
Christopher Zoppou & Steve Roberts
Abstract:
Dam-break problems involve the formation of shocks and
rarefaction fans. The performance of twenty explicit numerical
schemes used to solve the shallow water wave equations for
simulating the dam-break problems is examined. Results from these
schemes have been compared with analytical solutions to the
dam-break problem. Most of the numerical schemes produce
reasonable results for subcritical flows. Their performance for
problems where there is a transition between subcritical and
supercritical flows is mixed. Although many numerical schemes
satisfy the Rankine-Hugoniot condition, some produce solutions
which do not satisfy the entropy condition, producing non-physical
solutions. This was the case for the majority of first-order
schemes examined. Numerical schemes which consider sonic points
in the solution are guaranteed to produce entropy satisfying
solutions. Second-order schemes avoid the generation of expansive
shocks, however some form of flux or slope limiter must be used
to eliminate oscillations that are associated with these schemes.
These limiters increase the complexity and the computational
effort required, however they are generally more accurate than
their first-order counterparts. The limiters employed by these
second-order schemes will produce monotone or total variational
diminishing solutions for scalar equations. Some limiters do not
exhibit these properties when they are applied to the non-linear
shallow water wave equations. This comparative study shows that
there are a variety of shock-fitting numerical schemes that are
efficient, accurate and robust and suitable for solving the
shallow water wave equations when discontinuities are encountered
in the problem.
This service is maintained by the
Mathematical Sciences Institute (MSI)
Comments to
webmaster@maths.anu.edu.au
URL: http://wwwmaths.anu.edu.au/