平流扩散差分方程的新正定性重整化方案设计和试验

质量守恒是平流扩散差分方程所必须满足的基本性质,但是由于差分格式不具有正定性(positive-definite),因此在积分过程中负质量的产生会导致总质量不守恒.针对这一问题,本文从负质量产生的物理意义出发,提出了一个简单有效的新正定性重整化方案,通过点源平流扩散试验表明,该方案不但解决了平流扩散差分方程的正定性问题,同时保证了总质量守恒性.与WRF模式中采用的"重整化方案"相比,具有物理含义清楚、并且简单易行的优点.

Design and experiments of a new positive-definite renormalization scheme for advection-diffusion differential equation

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.