Hi,
I want to implement WENO reconstruction on characteristic variables.
Therefore, the following transformation between primitve and characteristic variables has to be defined:
W= P-1 V
where W is the characteristic variable vector,
V is the primitive variable vector
and P is the Jacobian matrix.
In the literature I saw it is common to write the above transformation as follows:
Wi= (Pi+1/2)-1 Vi
Pi+1/2 is to be evaluated at Vi+1/2 through arithmetic or Roe's average.
For this example, we choose fifth-order spatial accurate reconstruction and therefore the three stencils are being used:
S0=(i,i+1,i+2), S1=(i-1,i,i+1),S2=(i-2,i-1,i)
Then, one has to apply WENO reconstruction on Wi (characteristic vector) with the stencils indicated above and to get
WL,i+1/2 and WR,i-1/2 .
I encountered some difficulties in doing so and I got oscillations in the vicinity of discontinuities.
Hi,
The WENO reconstruction procedure is just an interpolation of different cell-values at the intercell face. Therefore, it does not matter what you are interpolating in terms of implementation, what means that the procedure is the same for either a reconstruction of the characteristic variables or the primitive ones. However, as stated by some authors, it is better to reconstruct the characteristic variables rather than the primitive ones. It has been found that the latter yields to a more oscillatory behavior (see Balsara et al.) even with monotonicity preserving non-oscillatory schemes. Please if you have not yet consulted the attached papers, give them a try since they are the basics for the implementation of WENO/MPWENO schemes. Hope this helps.
Best regards,
Bernat
Article Monotonicity Preserving Weighted Essentially Non-oscillatory...
Article WENO schemes based on upwind and centred TVD fluxes
It is best to carry out procedure in characteristic variables. The reasons are explained in e.g. 1987 ENO paper by Harten et al As to why i+1/2, not i, - because it has to be symmetric.
- Badges
- Science topic
- Similar topics
- Statistics
- Survey