The Weather Forecast Problem in Fluid Dynamics

This paper investigates the weather forecast problem in fluid dynamics through the lensof an Integral State-Dependent Coefficient Matrix (ISDCM) framework, resolving the persistent computational bottlenecks of classical numerical weather prediction (NWP). Traditionalatmospheric models rely on split-step approximations and explicit time-stepping schemesthat introduce severe numerical latency, truncation errors, and high energy drift over longforecast horizons. By re-engineering the non-linear primitive equations—derived from theNCAR WRF-ARW core—into an autonomous semilinear matrix structure (d⃗Ψdt = A(⃗Ψ)⃗Ψ),this study eliminates split-step delays and allows complex fluid cross-coupling physics toupdate concurrently. Evaluated over a 30-day forecasting horizon on standard consumerhardware, the ISDCMS pipeline successfully demonstrates stable phase-space trajectory convergence, achieving robust root mean square error (RMSE) metrics across core atmosphericvariables (such as a barometric column mass RMSE of 1.149 hPa and thermodynamic temperature RMSE of 1.848◦C), thereby establishing a lightweight, highly stable architecturefor fluid dynamic simulation