摘要
平流计算的精度对数值模式的结果有着重要影响。如何在半拉格朗日模式中发展高阶精度的标量平流计算方案是提高半拉格朗日数值模式精度的重要问题。文中采用计算流体力学中一个新的高精度正定保形的物质平流方案,通过映射单元格方法将其与半拉格朗日模式结合起来,既保留了半拉格朗日时间积分方案中积分时间步长大、计算效率高的特点,又发挥新方案高精度正定保形的平流计算优势。该新的标量平流方案是基于分段有理函数的高阶Godunov方案的变形,称之为Piecewise Rational Method(PRM)。此方案简单、实用,易于编程,可保持平流物理量的守恒。通过一维、二维理想试验,并与PPM(Piecewise Parabolic Method)和采用三次插值的半拉格朗日方案试验结果对比分析,表明物质平流方案对于空间变化幅度大的物理量具有较高的平流计算能力。与三次拉格朗日插值相比,物质平流方案的耗散性更小。与PPM方案相比,两者有不少相似之处,平流效果也几乎相当,但物质平流方案中采用的有理函数的保凸特性,且不需要界面值调整,在实现上相对简单。另外,通过将物质平流方案应用到GRAPES模式中的球面坐标系下的理想试验,进一步确认了物质平流方案的优点及在GRAPES模式中的可行性。
Accuracy of transport scheme has an important influence on the performance of a numerical weather prediction （NWP）model.How to develop a high-accuracy scalar transport scheme is of significance in improving the accuracy of the semi-Lagrangian model.This study applies a new high-order accuracy and positive-define conformal advection scheme into a semi-La-grangian model by using the cell-integrated scheme.It not only remains the large time step and high computational efficiency of the semi-Lagrangian time integration scheme,but also gives scope to the new advection scheme＇s advantages of high-order accuracy and positive define conformal computation.The new scalar advection scheme,named the Piecewise Rational Method （PRM）,is a deformation of the existing high-order Godunov scheme based on the piecewise rational function.This scheme is simple,practical and easy to program.It also can keep the scalar variables conservative in the advection process.The one-and two-dimensional ideal experiments were designed to test the PRM scheme.It is found that the PRM has great ability in treating the large spatial variations compared with the PPM（Piecewise Parabolic Method）and the cubic-Lagrangian interpolation method. The dissipation error of the PRM is smaller than that of the cubic-Lagrangian interpolation scheme.The PRM is much similar to the PPM with almost the same advection effect.But the PRM makes use of the convexity preserving nature of the rational function,and avoids the adjustments of the cell-interface values to enforce the monotonicity in the PPM.In addition,another ideal experiments were designed where the PRM is applied in place of the original water substances advection scheme utilized in the GRAPES model in the spherical coordinate system.The result further shows the advantages of the PRM and its feasibility in the GRAPES.
出处
《气象学报》
CAS
CSCD
北大核心
2011年第1期1-15,共15页
Acta Meteorologica Sinica
基金
国家973项目"我国南方致洪暴雨监测与预测的理论和方法研究"(2004CB418306)
国家科技支撑计划"灾害天气精细数值预报系统及短期气候集合预测研究"(2006BAC02B02)
自然科学基金面上项目(40675063)
关键词
平流
半拉格朗日
高精度
正定保形
Advection
Semi-Lagrangian
High-order accuracy
Positive-define conformal
