Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part I Spatial discretization
Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part I Spatial discretization
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DOI：
10.1016/j.jcp.2005.02.021
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发表时间：
2005-09
影响因子：
4.1
通讯作者：
Kyu Hong Kim;Chongam Kim
中科院分区：
文献类型：
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作者：
Kyu Hong Kim;Chongam Kim
通过对传统TVD限制器的分析，推导出一种新的多维限制函数，用于多维流动中的振荡控制。并利用多维极限函数建立了多维极限过程。MLP的主要优点是可以防止多维不连续性的振荡，并且它很容易与三阶以上的空间插值兼容。与其它高阶插值格式如ENO型格式相比，MLP格式在定常问题中具有良好的收敛性，且易于实现。在本文中，三阶和五阶插值方案与MLP，命名为MLP 3和MLP 5，开发和测试几个真实的应用。通过大量的算例（包括斜静止接触间断、膨胀扇、涡流、激波/涡干扰和粘性激波管问题）验证了MLP与M-AUSMPW+数值通量相结合在连续和间断流动中均显著提高了精度、效率和鲁棒性。通过将目前的方法扩展到三维流动，MLP有望进一步降低计算成本并提高精度。
Through the analysis of conventional TVD limiters, a new multi-dimensional limiting function is derived for an oscillation control in multi-dimensional flows. And, multi-dimensional limiting process (MLP) is developed with the multi-dimensional limiting function. The major advantage of MLP is to prevent oscillations across a multi-dimensional discontinuity, and it is readily compatible with more than third order spatial interpolation. Moreover, compared with other higher order interpolation schemes such as ENO type schemes, MLP shows a good convergence characteristic in a steady problem and it is very simple to be implemented. In the present paper, third and fifth order interpolation schemes with MLP, named MLP3 and MLP5, are developed and tested for several real applications. Through extensive numerous test cases including an oblique stationary contact discontinuity, an expansion fan, a vortex flow, a shock wave/vortex interaction and a viscous shock tube problem, it is verified that MLP combined with M-AUSMPW+ numerical flux substantially improves accuracy, efficiency and robustness both in continuous and discontinuous flows. By extending the current approach to three-dimensional flows, MLP is expected to reduce computational cost and enhance accuracy even further.