Physics – Mathematical Physics
Scientific paper
2012-01-02
Physics
Mathematical Physics
22 pages, 10 figures
Scientific paper
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions using difference invariants. While originally designed for constructing invariant finite difference schemes, we extend the usage of difference invariants to allow constructing of invariant finite volume methods as well. It is found that the classical invariant schemes converge to the Lagrangian formulation of the shallow-water equations. These schemes require to redistribute the grid points according to the physical fluid velocity, i.e. the mesh cannot remain fixed in the course of the numerical integration. Invariant Eulerian discretization schemes are proposed for the shallow-water equations. Instead of using the fluid velocity as the grid velocity, an invariant moving mesh generator is invoked in order to determine the location of the grid points at the subsequent time level. The numerical conservation of energy and mass is evaluated for the invariant and the non-invariant schemes. The invariant schemes constructed conserve the mass and momenta up to machine precision, similar as the non-invariant schemes but none of them is energy conserving.
Bihlo Alexander
Popovych Roman O.
No associations
LandOfFree
Invariant discretization schemes for the shallow-water equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Invariant discretization schemes for the shallow-water equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant discretization schemes for the shallow-water equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-55702