Could anyone suggest any papers that use the well-balancing approach, whereby an appropriate correction term is derived for numerical viscosity and used to balance the numerical flux and numerical source terms in the shallow water models?
I would try with the wonderfull book of Hinch (perturbation methods). The example is treated there.
I suggest you to read a good paper by Kurganov & Petrova (2007)
A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
Commun. Math. Sci.
Volume 5, Issue 1 (2007), 1-242
You can download it from http://projecteuclid.org/euclid.cms/1175797625
Thanks all.
Dear Vincent the book by Hinch does not treat conservative schemes.
Angelo, I have seen the reference you mentioned. I already have its improved version by the first author and others. It really makes sense but different from what I want. In the approach am looking for, one just has to use any numerical flux solver to substitute into the FV scheme, and directly use the full scheme to derive some correction terms for the numerical viscosity part of the flux. Then this correction term is added to the viscosity to achieve well balancing.
I suggest that you have a look at the ADER scheme. It has some nice properties and can be made high order.
Here is a reference but you can look more details in other articles on the web:
http://www.newton.ac.uk/preprints/NI06051.pdf
You may try pressman scheme or Abbott-Ionescu scheme. See so many papers on the web for both schemes. they are implemented in many softwares like MIKE11 and MIKE21.
I suggest you to read a paper by Qiuhua Liang and Fabien Marche (2009).
Numerical resolution of well-balanced shallow water equations
with complex source terms.
Advances in Water Resources
Here is the paper.
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