LAUSR

Atmospheric numerical models face long‐standing challenges in simulating mountain waves over steep topography, primarily due to numerical artifacts induced by traditional grid‐based methods. These artifacts include pressure‐gradient calculation errors, artificial wind fields, and spurious diffusion, which degrade simulation accuracy, especially in high‐gradient terrain regions. To address these issues, this study investigates the application of the cloud method (a meshless numerical approach) in non‐hydrostatic atmospheric models for simulating mountain waves over steep topography. The cloud method discretizes the computational domain using scattered points without predefined connectivity, avoiding the mesh distortion issues inherent in grid‐based methods. A series of numerical experiments was conducted to validate the method, including simulations of non‐hydrostatic mountain waves, waves over narrow mountains (half‐widths of 400, 200, and 100 m), static atmospheres over single‐peak and complex “Schär mountain” topography, high‐topography (4000‐ and 7000‐m peak height) flows, and adaptive point distribution tests. Comparisons with the traditional finite‐volume Monotonic Upwind centered Scheme for Conservation Laws (MUSCL) method (using terrain‐following (TF) coordinates) show that the cloud method simulates mountain waves stably even under extreme topographic steepness, avoiding the progressive wave distortion, flow detachment, and spurious vorticity observed in the MUSCL results. In static atmosphere tests, the cloud method eliminates artificial vertical velocity perturbations, reducing error magnitudes to the order of –. Additionally, its flexible adaptive point distribution achieves multiscale resolution without spurious artifacts at resolution interfaces, balancing computational efficiency and accuracy. This study demonstrates that the cloud method provides a robust and flexible alternative to traditional grid‐based approaches for steep topography simulations, with significant potential to improve operational weather prediction and climate modeling in complex terrain regions.