Achieving High-Order Convergence Rates with Deforming Basis Functions
Achieving High-Order Convergence Rates with Deforming Basis Functions
复制标题
通过变形基函数实现高阶收敛率
DOI：
10.1137/s1064827503425286
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
L. Rossi
中科院分区：
文献类型：
--
作者：
L. Rossi
本文研究了利用运动的、变形的椭圆高斯基函数来计算二维不可压缩流场中被动标量的演化。我们计算了计算单元的速度、旋转、扩展和变形的演化方程，作为流量的函数。我们发现，如果使用由基函数质心计算的物理流速数据，该方法只有二阶空间精度。然而，通过计算数值方法的残差，我们可以确定对质心数据的调整，从而使该方案达到四阶空间精度。具有非平凡流动参数的仿真表明，该方法具有理论预测的特性。
This article studies the use of moving, deforming elliptical Gaussian basis functions to compute the evolution of passive scalar quantities in a two-dimensional, incompressible flow field. We compute an evolution equation for the velocity, rotation, extension, and deformation of the computational elements as a function of flow quantities. We find that if one uses the physical flow velocity data calculated from the basis function centroid, the method has only second-order spatial accuracy. However, by computing the residual of the numerical method, we can determine adjustments to the centroid data so that the scheme will achieve fourth-order spatial accuracy. Simulations with nontrivial flow parameters demonstrate that the methods exhibit the properties predicted by theory.