守恒型有理函数插值半拉格朗日平流方案及性能分析

通过多种理想试验对正定、保形守恒型有理函数插值半拉格朗日平流方案分别在平面直角坐标以及阴阳网格球面坐标中进行了计算性能分析,并采用多种误差模对守恒型有理函数插值半拉格朗日平流方案的网格收敛性进行评估。结果表明,采用分段有理函数插值的守恒型半拉格朗日平流方案可以有效消除不连续分布处的数值振荡、保证正定性,物理场平滑分布时维持1-2阶收敛速度;而在不连续点或大梯度区域以及应用分维技术的多维算法都会通过有理函数的降阶特性,影响平流计算的收敛阶数,并且,在球面坐标中受球面曲率的影响,守恒型有理函数插值半拉格朗日平流算法的网格收敛速度有所降低。

Analysis of computational performance of the conservative Semi-Lagrangian with rational function advection scheme

Computational performance of the positive-definite shape-preserving conservative Semi-Lagrangian with rational funetion advection (CSLR) scheme is analyzed through a couple of idealized experiments in Cartesian plane coordinates and the spherical Yin-Yang coordinate system.Numerical convergence rate of the CSLR scheme is studied by using several error norms in both on-and two-dimensional computations.The numerical results reveal that the rational function adopted in the CSLR scheme eliminates numerical oscillation at discontinuous points,guarantees positive definition and acquires the 1st-2nd-order convergence rate in case of smooth distribution.At discontinuous points or steep-slope regions,in addition to the application of the multi-dimensional splitting algorithm,however, the convergence rate is reduced due to the special character of rational function.The convergence rate of the CSLR scheme decreases in the spherical coordinate because of the spherical curvature.