Universe Operating System (Universe OS): A Unified Conservation Framework for Cross-Scale Numerical Simulation and 2D Advection-Diffusion Modeling

Universe OS is a cross-scale, high-performance numerical simulation framework designed to address long-standing bottlenecks in traditional computational science—including poor numerical stability, inadequate energy conservation, and fragmented multi-domain solvers. Rooted in a self-consistent mathematical foundation and forced conservation design, the framework transforms scattered disciplinary fields into pluggable modules, enabling self-consistent full-scale simulation from microscopic particles to macroscopic fields. Its core advantage lies in a five-dimensional unified evolution operator that integrates spatial field quantities, energy, time, mass transport, and microscopic interactions into a single computational loop, achieving mathematical unification of all physical processes. Complemented by an energy account (Eₕₑₐₜ) for tracking numerical errors and a reality correction proxy (Zₚᵣₒₓᵧ) for error feedback, the framework ensures absolute total energy conservation in each simulation step, completely resolving numerical dissipation issues of traditional methods. For micro-macro coupling, complex particle behaviors (e.g., injection ηᵢₙ, fusion ηբᵤₛ) are converted into macroscopic field contributions via microscopic agents (Nₑₓₚₑᶜₜ) and Monte Carlo sampling, avoiding the high cost of traditional molecular dynamics/quantum simulations. As a core application module, the AdvectionDiffusion2D class supports adaptive time steps (based on CFL conditions), multiple boundary conditions (periodic, Dirichlet, Neumann), third-order upwind-biased polynomial reconstruction with TVD limiters, and optional Crank-Nicolson implicit diffusion (with SciPy fallback). It includes energy tracking, observation hooks, and core methods for single-step simulation, batch running, point probing, regional integration, and Fourier spectrum analysis. The framework also features extended components such as a Flask-based RESTful API for observation, adaptive time-step logging, and plotting tools, alongside comprehensive testing (boundary condition verification, energy conservation tests) and performance benchmarking. Packaged as a lightweight, open-source, and free-to-use tool, Universe OS shifts scientific research focus from "solver construction" to "domain knowledge modeling," ending the era of "reinventing the wheel" in computational fields. It is applicable to fluid mechanics, heat transfer, magnetohydrodynamics, particle physics, and astrophysics/cosmology, laying the foundation for interdisciplinary research and engineering applications.