An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension
An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension
复制标题
DOI：
10.1175/1520-0493(2001)129
复制
发表时间：
2001-02
影响因子：
3.2
通讯作者：
T. Yabe;R. Tanaka;T. Nakamura;F. Xiao
中科院分区：
文献类型：
--
作者：
T. Yabe;R. Tanaka;T. Nakamura;F. Xiao
摘要：提出了两种能精确保证质量守恒的半拉格朗日格式。尽管它们呈非守恒形式，但插值函数是在通过重映射拉格朗日体积来推进的单元积分值（质量）守恒的约束条件下构建的。因此，所得格式对每个计算网格单元都能保证质量守恒。其中一种（CIP - CSL4）是原始的三次插值传播（CIP）方法的直接扩展，在该方法中，使用三次多项式作为插值函数，并根据微分平流方程计算梯度。在CIP - CSL4方法中采用四阶多项式作为插值函数，并将质量守恒作为对插值剖面重构的一个附加约束条件。在另一种格式（CIP - CSL2）中，CIP原理应用于积分质量，插值函数变为二次函数。后一种格式可以很容易地扩展……
Abstract Two semi-Lagrangian schemes that guarantee exactly mass conservation are proposed. Although they are in a nonconservative form, the interpolation functions are constructed under the constraint of conservation of cell-integrated value (mass) that is advanced by remapping the Lagrangian volume. Consequently, the resulting schemes conserve the mass for each computational grid cell. One of them (CIP–CSL4) is the direct extension of the original cubic-interpolated propagation (CIP) method in which a cubic polynomial is used as the interpolation function and the gradient is calculated according to the differentiated advection equation. A fourth-order polynomial is employed as the interpolation function in the CIP–CSL4 method and mass conservation is incorporated as an additional constraint on the reconstruction of the interpolation profile. In another scheme (CIP–CSL2), the CIP principle is applied to integrated mass and the interpolation function becomes quadratic. The latter one can be readily extend...