“...it describes a new and easy-to-implement technique to solve accurately hyperbolic systems of conservation laws with source terms (balance laws) with clear and comprehensive explanations.”

I think it is because it describes a new and easy-to-implement technique to solve accurately hyperbolic systems of conservation laws with source terms (balance laws) using clear and comprehensive explanations. This field has been further developed by various senior researchers in Europe and in the USA. It is still under development for specific remaining—but hard!—problems, such as nonlinear resonance, on which I published results in collaboration with Drs. Debora Amadori of the University of L’Aquila and Graziano Guerra of the University of Milano Bicocca.

This paper contains parts of my Ph.D. thesis results. This work was done during the 1995-97 period in an industrial context for the French Atomic Energy Commission. It was motivated by concrete needs as defined by the engineers working there who were asking for serious improvements for practical calculations—namely, incidental simulations in nuclear plants. It also turned out to be very useful for shallow water problems, especially for dam-break simulations.

It explains, in a founded mathematical sense, the right way to modify numerical schemes for conservation laws in order to properly handle source terms on the right-hand side while maintaining important theoretical properties of the model.