[linkamp]

Hi everyone,
I have a pretty basic question, it might be just a matter of nomenclature but neither literature nor talking to people dealing with CFD for hyperbolic systems got me a satisfying answer. The question is just as in the topic: Is there a difference between so-called characteristic based schemes and Riemann solvers? Both terms occur in literature and I cannot make out the difference even though the terms are not used synonymously and sometimes even contrarily.
Both are schemes definitely based on the same derivation, transorm into normal form -> solve system of ODE. Despite the possibility of application of Riemann solvers on FV-schemes I'm curious about the difference in FD formulation. In Toro's "Riemann Solvers and Numerical methods for Fluid Dynamics" (p168ff) the first order upwind scheme is described using the Riemann Invariants, which is exactly what is referred to in literature as"method of characteristics" or "characteristic based FD-scheme".

Hoping I have made my point (or questionmark) clear, can anyone give me an answer or recommend literature where the difference (if exists) is explained?

Thanx in advance

[FMDenaro]

I cannot be sure about the difference in literature but "Riemann invariant" exist only for omoentropic flow conditions while the existence of characteristic curves are more general in hyperbolic equations.
In general flow conditions (for example isoentropic flow), you could define Riemann variables that, however, are not constant along the characteristic curves

[linkamp]

Thanks for the fast reply

Originally Posted by FMDenaro

I cannot be sure about the difference in literature but "Riemann invariant" exist only for omoentropic flow conditions while the existence of characteristic curves are more general in hyperbolic equations.

Talking about Riemann "invariants" you are right and the restriction is even stronger, because the Riemann variables are only invariant in case of homentropic/isentropic (linearized in energy) in the (mass and momentum) linear case because in case of nonlinear Euler equations linear (undisturbed) superposition is not possible.

Originally Posted by FMDenaro

In general flow conditions (for example isoentropic flow), you could define Riemann variables that, however, are not constant along the characteristic curves

Agree as well. The Riemann variables are physically not constant along the characteristic line (in the nonlinear case), but are assumed to be for the sake of explicit time integration. However both terms "characteristic based scheme" and "Riemann solver" are used for schemes applied to nonlinear equations.

[FMDenaro]

however, the book of LeVeque should be suitable to better define the difference in the nomenclature