A class of approximate Riemann solvers and their relation to relaxation schemes

By Randall J. LeVeque, M. Pelanti. 2001

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Finite Volume Methods: Foundation and Analysis (2004, methodology): “The relaxation scheme can be reinterpreted as defining a particular approximate Riemann solver for the original system conservation laws, see LeVeque and Pelanti, 2001.”
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions (2002, methodology): “In particular, this seems to be a more robust approach than the quasi-steady wave-propagation algorithm proposed in [21], as noted in [23].”
Tsunami modelling with adaptively refined finite volume methods* (2011, unknown): “The approach outlined above that splits the jump in q and in f(q) is also related to the relaxation approaches discussed in Bouchut (2004) and LeVeque and Pelanti (2001).”
GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION (2010, methodology): “However, it is interesting to see that the resulting scheme can be obtained from a quite different approach, using first ideas introduced in [8] for the Euler equation with gravity in the case without friction (α = 0), together with relaxation schemes (note that the relation between approximate Riem”