A GPU-Ready LMARS-Based Nonhydrostatic Dynamical Core with a Monotonicity Limiter and a Vertical Implicit Solver

Global numerical modeling is entering the era of kilometer-scale, non-hydrostatic, and AI-powered. Meanwhile, heterogeneous computing is the trend in HPC. As a strong candidate for the next-generation global kilometer-scale GCM, the A-grid dynamical core based on LMARS (Low Mach number Approximate Riemann Solver) needs to address the following three issues: 1. The strong-gradient problem is particularly significant at high resolutions. Although LMARS can use higher-order numerical schemes, it cannot guarantee monotonicity. 2. The large discrepancy between vertical and horizontal grid spacings severely limits the time integration step size of the non-hydrostatic model. 3. Classic models are written in FORTRAN, and algorithms designed for CPUs may not be suitable for GPUs. This study builds a prototype model LMARSpy with specific solutions to these issues: addressing the strong-gradient problem through a high-order monotonicity limiter, to solve the non-hydrostatic problem with a conserving vertical implicit solver, and building a Python-based high-performance computing platform to address heterogeneous computing challenge. A series of benchmark tests show that: 1. The monotonicity limiter effectively eliminates non-physical oscillations and maintains high-order accuracy in discontinuous regions, with a computational cost increase of only 10.4% on GPUs. 2. The vertical implicit solver relaxes CFL limitations in cases where vertical grid spacing is much larger than horizontal grid spacing, improving computational efficiency by at least an order of magnitude. 3. The Python high-performance computing platform supports the efficient operation of the dynamical core on both CPU and GPU computing platforms. The performance of a single GPU-based system can rival large computing clusters with over 325 standard CPU cores. Last but not least, with the PyTorch backend built-in, LMARSpy is born with efficient compatibility with machine learning.