To address the pressing demand for high-precision fluid dynamics reconstruction in applications such as virtual reality and augmented reality, this study proposes a real-time smoke reconstruction framework based on global physical priors. The framework overcomes the core challenges of traditional methods, including poor physical consistency under sparse views and low computational efficiency. The research team integrates differentiable fluid simulators and differentiable renderers to build an end-to-end optimization system. Innovations include the use of divergence-free Laplacian eigenfunctions as velocity field bases, eliminating the reliance on linear solvers in traditional pressure projection processes and achieving a balance between physical constraints and computational efficiency.