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note that it works just fine with compressible_rk using RK4 integration, so the issue seems to be the spatial reconstruction, not the temporal evolution. I suspect that the problem is that the 4th order stencils don't work because we are passing in cell-averages and then we need to do HSE integration on the cell averages, but we are treating them like cell-centers.
Not sure why, but they seem to cause the Rayleigh-Taylor to life up as time evolves.
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