平流扩散差分方程的新正定性重整化方案设计和试验  

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

作　　者：郝世峰 崔晓鹏[2] 

机构地区：[1]浙江省气象台,杭州310017 [2]中国科学院大气物理研究所云降水物理与强风暴实验室,北京100029

出　　处：《物理学报》2012年第3期561-568,共8页Acta Physica Sinica

基　　金：国家重点基础研究发展计划项目(批准号:2009CB421505);浙江省气象局开放专项(批准号:kf2007007);浙江省科技厅面上科研社会发展项目(批准号:2008C23012);国家自然科学基金海峡两岸合作研究项目(批准号:40921160379)资助的课题~~

摘　　要：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(posirive-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.Total mass conservation is a basic property of advection-diffusion differential equation.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.

关 键 词：正定性 重整化方案 质量守恒 

分 类 号：O241.82[理学—计算数学] P401[理学—数学]