Comparison between multilayer Saint-Venant system and Navier-Stokes equations.
References:
[1]
Audusse E., Bristeau M.O.,
A Well-balanced Positivity Preserving "Second-order" Scheme
for Shallow Water Flows on Unstructured Grids,
to appear in JCP (2005).
[2]
Audusse E., Bouchut F., Bristeau M.O., Klein R., Perthame B.,
A Fast and Stable Well-balanced Scheme with Hydrostatic Reconstruction
for Shallow Water Flows,
SIAM J. of Sc. Comp. 25 (2004), no. 6, 2050-2065.
[3]
Audusse E., Bristeau M.O.,
Transport of Pollutant in Shallow Water Flows :
A Two Time Steps Kinetic Method,
M2AN 37 (2003), no.2, 389-416.
[4]
Audusse E.,
A multilayer Saint-Venant System :
Derivation and Numerical Validation,
DCDS-B, Vol. 5 (2005), no. 2, 189-214.
Comments:
Shallow water equations solver is based on
a kinetic interpretation of the homogeneous system (stability)
coupled with a hydrostatic reconstruction on the interface
to take into account the presence of the source terms
(well-balancing).
For the transport equation, a kinetic solver is used.
It uses the mass fluxes
of the hydrodynamic part (stability)
but it has its own time step (efficiency).
The multilayer solver is based on a kinetic interpretation
of the enlarged system.