Extending Gal-Chen and Somerville terrain-following coordinate transformation on time-dependent curvilinear boundaries

The classical terrain-following coordinate transformation of Gal-Chen and Somerville has been extended to a broad class of time-dependent vertical domains. We provide explicit formulae for the associated transformation coefficients which are readily applicable to numerical implementations. The proposed extension facilitates modeling of undulating boundaries in various areas of computational fluid dynamics. The implementation is discussed in the context of a nonhydrostatic anelastic model for simulations of atmospheric and oceanic flows. The theoretical development is illustrated with numerical simulations of idealized flows. We also discuss an example of a practical application which incorporates a long-wave-approximation for a finite-amplitude free-surface upper boundary, directly relevant to ocean models.