A limiter for PPM that preserves accuracy at smooth extrema

We present a new limiter for the PPM method of Colella and Woodward [4] that preserves accuracy at smooth extrema. It is based on constraining the interpolated values at extrema (and only at extrema) using nonlinear combinations of various difference approximations of the second derivatives. Otherwise, we use a standard geometric limiter to preserve monotonicity away from extrema. This leads to a method that has the same accuracy for smooth initial data as the underlying PPM method without limiting, while providing sharp, non-oscillatory representations of discontinuities.