Examples incorporating source terms into Riemann solvers, as described in
Balancing Source Terms and Flux Gradients in High-Resolution
Godunov Methods
Randall J. LeVeque, J. Comput. Phys. vol 146 (1998) pp. 346-365.
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and
Wave Propagation Methods for Conservation Laws with Source Terms
Randall J. LeVeque and Derek S. Bale, to appear in Proc.
7'th Intl. Conf. on Hyperbolic Problems, Zurich,
February 9-13, 1998.
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See also Section 5.5 of Computational Methods for Astrophysical Fluid Flow