High order spectral volume method for multi-component flows
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摘要: 针对高维及多物理耦合计算耗费大等困难，设计适合多介质流动模拟的模板紧致、易于并行、高阶精度、计算耗费小的谱体积方法。该方法是求解双曲型守恒率谱体积方法的直接推广，针对多介质流动物质界面捕捉的困难，利用拟守恒格式的思想避免物质界面处的非物理振荡。数值模拟结果表明，本方法具有高阶精度、高分辨率，且节约计算量，并且可以有效避免物质界面处非物理振荡。Abstract: Numerical simulation of multi-material flows has been an important issues in CFD, and most CFD production codes used for multi-material flow simulation is of either first or second order accuracy, too inefficient and costly with its grid refinement for high accuracy required problems. In this paper, a high-order, efficient, compact method, called the spectral volume method, was developed for the simulation of the multi-material flow as an extension of the spectral volume method for the conservation laws. It has been pointed out that the conservative spectral volume method for the multi-material flow will cause oscillation, and the reason for this has been analyzed. So the idea of quasi-conservative scheme was borrowed to prevent the spurious oscillations in the vicinity of a material contact discontinuity. Several numerical experiments proved that there is no oscillation near the material interface and the result also demonstrates the accuracy, the efficiency and the high performance of the scheme for the multi-material flow simulation.
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Key words:
- fluid mechanics /
- spectral volume method /
- high order /
- stiffened gas /
- multi-component flows /
- compact stencil
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图 1 守恒谱体积格式的一维多介质运动界面问题
Figure 1. One-dimensional moving interface problem for conservative spectral volume scheme
图 2 拟守恒谱体积格式的一维多介质运动界面问题
Figure 2. One-dimensional moving interface problem for quasi-conservative spectral volume scheme
图 3 拟守恒谱体积格式的高压力比气液激波管问题
Figure 3. High pressure ratio gas-liquid shock tube problem for quasi-conservative spectral volume scheme
图 4 拟守恒谱体积格式的高压力比气液激波管问题
Figure 4. High pressure ratio gas-liquid shock tube problem for quasi-conservative spectral volume scheme
图 5 拟守恒谱体积格式的三点问题密度等值线图
Figure 5. Density contours of triple point problem for quasi-conservative spectral volume scheme
表 1 格式的数值精度
Table 1. Numerical accuracy of present schemes
N Lerr1 order Lerr1 order Lerr1 order Lerr1 order k=2 k=3 k=4 k=4 10 4.80×10-3 - 3.91×10-4 - 7.22×10-6 - 4.69×10-7 - 20 1.17×10-4 2.04 6.77×10-5 2.53 4.34×10-7 4.06 1.93×10-8 4.60 40 2.93×10-5 2.00 9.64×10-6 2.81 2.47×10-8 4.14 6.79×10-10 4.83 80 7.34×10-5 2.00 1.26×10-6 2.94 1.56×10-9 3.98 2.21×10-11 4.94 160 1.84×10-5 2.00 1.59×10-7 2.99 9.77×10-11 4.00 6.85×10-13 5.01 
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