Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics
Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics
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DOI：
10.1016/j.jcp.2007.11.031
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发表时间：
2008-02
期刊：
影响因子：
--
通讯作者：
Y. Imai;T. Aoki;K. Takizawa
中科院分区：
文献类型：
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作者：
Y. Imai;T. Aoki;K. Takizawa
该方案是插值微分算子方案（IDO-CF）的保守形式，可以为可压缩和不可压缩流体方程提供高精度解。具有四阶精度的空间离散化是从由单元积分值和点值局部构造的插值函数导出的。通过求解单元积分值的通量形式和点值的导数形式的流体方程，对这些值进行耦合和时间积分。 IDO-CF方案精确地守恒了质量、动量和能量，比IDO方案的非守恒形式更保留了高分辨率。湍流的直接数值模拟的精度与光谱方法相当。黎曼问题和盖驱动腔流的基准测试表明，IDO-CF 方案在可压缩和不可压缩流体动力学研究中具有巨大的前景。
The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.