Design and experiments of a new positive-definite renormalization scheme for advection-diffusion differential equation
平流扩散差分方程的新正定性重整化方案设计和试验

Total mass conservation is a basic property of advection-diffusion differential equation. While since the difference schemes is not positive-definite, total mass is not conserved, caused by negative mass in numerical integration. Aiming at this problem, a new positive-definite renormalization scheme is proposed based on the physical meaning of negative mass. Experiments of point-source advection-diffusion show that the new renormalization scheme not only solves the positive-definite problem of advection-diffusion differential equation, but also keeps the property of total mass conservation. Compared with the renormalization scheme in the WRF model, the new positive-definite renormalization scheme has virtues of clear physical meaning and easier mannpulation.