I am currently working on a scheme that uses finite differences WENO5-Z with 3rd Order Runge-Kutta time integration for solving the Euler equations. The code projects the conserved variables and fluxes onto the eigenspace using Roe-averages at i+1/2 and uses a local Lax-Friedrichs flux splitting before applying the WENO reconstruction to the interface fluxes.
When I perform several numerical test (Sod Problem, Modified Sod, and Lax Problem) I get a spurious behavior in the left-traveling rarefaction wave (looks a lot like an expansion shock) in two of them, specifically in the Sod and Lax Problem. The lax problem also displays an oscillatory behavior in across the contact discontinuity.
I attached below the plots for the density, pressure, and velocity. I was wondering if any of you have encountered this issue before. I am surprised to see that kind of behavior since I am implementing Lax-Friedrichs flux splitting. Thank you very much in advance for your help!