Pressure Decimation and Interpolation (PDI) method for a baroclinic non-hydrostatic model

Non-hydrostatic models are computationally expensive in simulating density flows and mass transport problems due to the requirement of sufficient grid resolution to resolve density and flow structures. Numerical tests based on the Non-Hydrostatic Wave Model, NHWAVE (Ma et al., 2012), indicated that up to 70% of the total computational cost may be born by the pressure Poisson solver in cases with high grid resolution in both vertical and horizontal directions. However, recent studies using Poisson solver-based non-hydrostatic models have shown that an accurate prediction of wave dispersion does not require a large number of vertical layers if the dynamic pressure is properly discretized. In this study, we explore the possibility that the solution for the dynamic pressure field may, in general, be decimated to a resolution far coarser than that used in representing velocities and other transported quantities, without sacrificing accuracy of solutions. Following van Reeuwijk (2002), we determine the dynamic pressure field by solving the Poisson equation on a coarser grid and then interpolate the pressure field onto a finer grid used for solving for the remaining dynamic variables. With the Pressure Decimation and Interpolation (PDI) method, computational efficiency is greatly improved. We use three test cases to demonstrate the model's accuracy and efficiency in modeling density flows.