Well-balanced compressible cut-cell simulation of atmospheric flow

Area of Science:

• Computational Fluid Dynamics
• Atmospheric Science
• Numerical Methods

Background:

• Terrain-following coordinates struggle with steep topographic gradients in atmospheric simulations.
• Accurate representation of topography is crucial for simulating atmospheric flows.

Purpose of the Study:

• To present an explicit, two-dimensional numerical method for atmospheric flow simulations on cut-cell meshes.
• To address limitations of existing methods in representing complex topography.

Main Methods:

• Developed an explicit, fully conservative numerical scheme for atmospheric flow equations on cut-cell meshes.
• Employed a dimensionally split framework for independent solution of coordinate directions.
• Incorporated well-balanced gravitational sources for stable near-hydrostatic flow simulations.

Main Results:

• The method allows time steps determined by regular grid spacing, avoiding stability issues from boundary cells.
• Demonstrated conceptual and practical simplicity and flexibility in flux approximation.
• Successfully applied the method to simulate buoyant bubble rise and lee-wave generation.

Conclusions:

• The presented explicit numerical method offers a robust and efficient alternative for atmospheric flow simulations on cut-cell meshes.
• The scheme's features facilitate stable and accurate modeling of flows over complex terrain.