高阶正定守恒的中心约束多矩有限体积平流模式  

A high order positive-definite conservative multi-moment center constrained finite volume transport model

作　　者：舒谦 唐杰[2,3] 陈春刚 肖锋[5] 沈学顺[2,3] 周立隆[2,3] 李泽椿 朱克云 李兴良 SHU Qian;TANG Jie;CHEN Chungang;XIAO Feng;SHEN Xueshun;ZHOU Lilong;LI Zechun;ZHU Keyun;LI Xingliang(Chengdu University of Information Technology,Chengdu 610225,China;Numerical Weather Prediction Center of CMA,Beijing 100081,China;National Meteorological Center,Beijing 100081,China;Xi'an Jiaotong University,Xi'an 710049,China;Department of Mechanical engineering,Tokyo Institute of Technology,Tokyo 152-8850,Japan)

机构地区：[1]成都信息工程大学,成都610225 [2]中国气象局数值预报中心,北京100081 [3]国家气象中心,北京100081 [4]西安交通大学,西安710049 [5]日本东京工业大学机械工程系,东京152-8850

出　　处：《气象学报》2020年第4期665-678,共14页Acta Meteorologica Sinica

基　　金：国家重点研发计划项目(2017YFA0603901、2017YFC1501901);北京市杰出青年科学家基金项目(JQ18001)。

摘　　要：采用新的均匀三点中心约束多矩有限体积方法(3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints,MCV3_UPCC),发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值(最小值为0时则保持数值正定)与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。A two dimensional 3rd order positive-definite conservative advection model is developed in this study based on the novel 3-point multi-moment constrained finite-volume scheme for uniform points with center constraints(MCV3_UPCC).In the context of 3-point multi-moment finite volume method,three equidistant solution points are defined within a single cell and the time evolution equations can be obtained by flux form formulation.The multi-moment constraints in this novel scheme are imposed at the cell center on the point value,the first and second order derivatives,and a polynomial of 4th degree can then be reconstructed in a single cell.The resulting MCV3_UPCC scheme has 3rd order accuracy and ensures the exact numerical conservation due to the continuity of the flux function at cell interfaces.To suppress the numerical oscillations and the positivity of certain physical quantities,the boundpreserving limiting projection is introduced into the new MCV3_UPCC scheme,which satisfies the minimum and maximum principle.The new positive-definite conservative advection model is validated by widely used benchmarks.The presented transport model has a good accuracy in comparison with other existing high-order models,and it has the potential to be applied in real moist transport model.

关 键 词：平流方案 多矩有限体积法 正定守恒 高精度方案 

分 类 号：P435[天文地球—大气科学及气象学]