We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...
We present one- and two-dimensional central-upwind schemes
for approximating solutions of the Saint-Venant system
with source terms due to bottom topography.
The Saint-Venant system has steady-state solutions
in which nonzero flux gradients are exactly balanced by
the source terms. It is a challenging problem to preserve
this delicate balance with numerical schemes.
Small perturbations of these states are also very difficult
to compute. Our approach is based on extending semi-discrete central...
We present a family of high-order, essentially non-oscillatory,
central schemes for
approximating solutions of hyperbolic systems of conservation laws.
These schemes are based on a new centered version of the Weighed
Essentially Non-Oscillatory (WENO) reconstruction of point-values
from cell-averages, which is then followed by an accurate approximation
of the fluxes a natural continuous extension of Runge-Kutta solvers.
We explicitly construct the third and fourth-order scheme and demonstrate...
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