[AdrianN]

Hi all,

I would like to know if it is possible to construct WENO-ADER schemes for the resolution of linear wave propagation in heterogeneous media.

As far as I know, WENO-RK schemes can be applied to such a problem by taking into account that a characteristic-wise, instead of component-wise, WENO reconstruction must be done. Otherwise, it is not possible to account for variations in the media, that is, in the flux matrices. This technique is outlined in David I. Ketcheson et al.: High-Order Wave Propagation Algorithms for General Hyperbolic Systems.

Considering again WENO-ADER schemes, in this case, unlike in Runge Kutta methods, high order in time is achieved by means of reconstructing time derivatives in terms of spatial derivatives using the Cauchy-Kowalevksi (CK) procedure. Is it neccessary to account for the variations of the media in the CK procedure? (Which I do not figure out how to do it). Or... could it be sufficient just to carry out the characteristic-wise WENO reconstruction? (And then doing the CK procedure conventionally considering the flux matrices constant).

Thanks for the help

[FMDenaro]

I don't know if that can help you but in the Leveque's book, section 21.5, this problem is illustrated by using Riemann problems. You could also check in its Clawpack software some methods that can help you.

[AdrianN]

Dear Filippo,

thanks for the comments. I will have a look though I think they only show the first order approach.