In this talk, we will discuss a family of flux limiters for high order finite difference WENO methods solving compressible Euler equations. This family of flux limiters are generalized from maximum principle preserving flux limiters applied to high order methods solving scalar conservation laws. Its origin can be found through the Flux Corrected Transport method (low order, local maximum principle preserving) developed by Boris and Book. We will discuss the algorithm and some of the major issues we try to address.
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