Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields

A methodology is presented for simulation of strongly non-Gaussian random fields. It involves an iterative scheme that produces sample functions that match a prescribed non-Gaussian marginal distribution and a prescribed Spectral Density Function (SDF). The simulated field possesses all the properties of translation fields. The methodology also determines the SDF of an underlying Gaussian field according to translation field theory. This is the latest development in a class of simulation algorithms that are presented and critically reviewed. Several numerical examples are provided demonstrating the capabilities of the methodology, comparing it with three previous algorithms, and determining the limits of its applicability. Compared to earlier algorithms, the proposed methodology provides increased accuracy at a fraction of the computational cost.