Abstract

Robust, accurate, and efficient numerical methods are essential for reliable climate and weather prediction. One promising approach is to design schemes that preserve key mathematical and physical structures of the underlying equations, such as conservation laws, balance relations, stability properties, and energy or entropy constraints. Preserving these structures at the discrete level can have a profound impact on the robustness and fidelity of atmospheric simulations.

In this talk, we present a hierarchy of atmospheric models of increasing complexity, together with structure-preserving numerical methods tailored to each system. This hierarchy provides a pathway for understanding how discrete conservation, stability, and balance properties can be maintained as models progress from idealised equations toward more realistic atmospheric dynamics, including compressible and moist multiphase atmospheric flows.