A New Mass, Energy, Vorticity, and Potential Enstrophy Conserving Scheme for Complex Boundaries in 3D Nonhydrostatic Stretched or Nested Grid Models

We present a new generalization of a mass, energy, vorticity, and potential enstrophy conserving boundary scheme developed for the 2D shallow water equations (SWEs) to the governing equations for 3D nonhydrostatic atmospheric flows. The boundary scheme for the 2D SWEs involves solving specially formulated evolution equations for the vorticity at boundaries and extrapolation formulas for the fluid depth at boundaries. We generalize this scheme to 3D flows by solving evolution equations for each of the three components of the vorticity along boundaries and using extrapolation formulas to obtain the air density at boundaries. The boundary scheme can use either stairsteps or shaved cells to approximate fluid-land boundary profiles (with the shaved-cell approximation being one order more accurate than the stairstep approximation). We perform numerical simulations to demonstrate the scheme's conservation properties and accuracy and show results from an application to a realistic urban-scale street geometry. The scheme is useful because it conserves several important domain-summed quantities in flows around obstacles of arbitrary shape such as buildings and complex topography.