A new adiabatic kernel for the MC2 model

Abstract

Traditional semi‐implicit formulations of nonhydrostatic compressible models may not be stable in the presence of steep terrain when pressure gradient terms are split and lagged in time. If all pressure gradient terms and the divergence are treated implicitly, the resulting wave equation for the pressure contains off‐diagonal cross‐derivative terms leading to a highly nonsymmetric linear system of equations. In this paper we present a more implicit formulation of the Mesoscale Compressible Community (MC2) model employing a Generalized Minimal Residual (GMRES) Krylov iterative solver and a more efficient semi‐Lagrangian advection scheme. Open boundaries now permit exact upwind interpolation and the ability to reproduce simulations to machine precision is illustrated for one‐way nesting at equivalent resolution. Numerical simulations of hydrostatic and nonhydrostatic mountain waves demonstrate the stability and accuracy of the new adiabatic kernel. The computational efficiency of the model is reported for 1D Jacobi and 3D Alternating Direction Implicit (ADI) line relaxation preconditioned implemented with a parallel data transposition strategy.