Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation
Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation
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DOI：
10.1016/j.jcp.2005.05.011
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发表时间：
2005-12
影响因子：
4.1
通讯作者：
M. Popescu;W. Shyy;M. Garbey
中科院分区：
文献类型：
--
作者：
M. Popescu;W. Shyy;M. Garbey
在开发适合计算气动声学的数值技术时，Tam和同事提出的色散关系保持（DRP）方案以及Ashcroft和Zhang提出的优化预因子紧致（OPC）方案都显示出降低耗散和色散误差的理想特性。这些方案，最初基于有限差分，试图优化系数，以更好地分辨短波相对于计算网格，同时保持预先确定的精度的形式顺序。在本研究中，提出了两种方案的有限体积公式，以更好地处理在许多工程应用中遇到的非线性和复杂几何。采用有和无粘性耗散的线性和非线性波动方程作为试验问题。重点介绍了这些方法的主要特点，并利用不同波长的线性和非线性波动方程作为测试用例，记录了这些方法的性能。对于线性波动方程，DRP和OPC格式之间没有太大的区别。对于非线性波动方程，DRP和OPC格式的有限体积版本在高梯度或不连续区域提供了更好的解。
In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.