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We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law on a closed Riemannian manifold M.
For an initial value in BV(M) we will show that these schemes converge with a convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to
A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
The motion of an incompressible fluid confined to a shallow basin with
a slightly varying bottom topography is considered. Coriolis force,
surface wind and pressure stresses, together with bottom and
lateral friction stresses are taken into account. We introduce
appropriate scalings into a three-dimensional anisotropic eddy
viscosity model; after averaging on the vertical direction and
considering some asymptotic assumptions, we obtain a two-dimensional
model, which approximates the three-dimensional...
First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a -point monotone scheme may give an oscillatory solution even though...
First–order accurate monotone conservative schemes have good
convergence and stability properties, and thus play a very
important role in designing modern high resolution shock-capturing
schemes.
Do the monotone difference approximations always
give a good numerical solution in sense of monotonicity preservation
or suppression of oscillations? This note will investigate this problem
from a numerical point of view and show that
a (2K+1)-point monotone scheme may give an oscillatory solution
even...
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