Abstract:
Three recently proposed compact WENO limiters, including the simple WENO limiter,
p-weighted WENO limiter and the multi-resolution WENO limiter, are studied in the flux reconstruction framework. The WENO limiter is able to simulate the flow with a relatively high resolution and capture the shock wave. They are compact since the reconstruction expands only the trouble cell and its neighbors. The positivity-preserving limiter is applied to avoid negative density/pressure near the shock. Based on unstructured quadrilateral cells, the three WENO limiters in the flux reconstruction framework are compared in multiple cases including the double Mach reflection, strong shock/vortex interaction, shock reflection, viscous bow shock and shock/laminar boundary layer interaction. The results show that, both the multi-resolution WENO limiter and the
p-weighted WENO limiter are able to simulate the flow field with a relatively high resolution and capture the shock wave. The spurious oscillations near the shock due to the intrinsic numerical instability of the flux reconstruction method are suppressed by the multi-resolution WENO and the p-weighted WENO limiter. Compared to the multi-resolution WENO limiter, the
p-weighted WENO limiter shows a better convergence property. The simple WENO limiter leads to the worst result among the three WENO limiters. The results also show that the WENO limiters call for a better shock sensor to achieve convergence.