A pseudo arc-length method for strong discontinuity of detonation wave and its man manufactured solution verification
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摘要: 针对该问题开展了伪弧长数值算法研究，通过引入弧长参数，使网格按照一定的形式自适应移动，达到在强间断区域自动加密的效果，从而提高网格分辨率。基于伪弧长算法编写了二维程序，并对程序进行人为解方法验证。将伪弧长算法和直接有限体积法的数值结果进行对比，通过误差分析，显示出伪弧长算法能有效提高计算精度。最后将伪弧长算法应用于气相爆轰波在二维管道中的传播问题，研究了波阵面的捕捉效果和爆轰波胞格结构的形成过程。Abstract: In this paper we studied a pseudo arc-length method for high-precision and high-resolution calculation, a problem that has been a great challenge for numerical simulation of strong discontinuity for explosion shock wave. By the introduction of the arc-length parameters, the mesh will move adaptively and gather automatically in the strong discontinuity singular areas, which will help to improve the grid resolution. We wrote 2D programs based on theoretical work, and conducted the program verification using the man maufactured solution. Through error analysis and numerical results, it was demonstrated that this method was more efficient in improving the calculation accuracy than the finite volume method. Finally we applied the pseudo arc-length method to 2D gas detonation wave propagation problems and studied the capture effect in the wave front and the formation of detonation cellular structure.
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表 1 有限体积法与伪弧长算法在不同网格数时的误差和精度
Table 1. Numerical errors and precision of FVM and PALM changing with grid numbers
网格数 ε O 有限体积法 伪弧长算法 有限体积法 伪弧长算法 40×40 0.138 338 0.219 237 80×80 0.055 447 0.073 144 1.319 0 1.583 7 160×160 0.015 964 0.019 735 1.796 3 1.889 9 320×320 0.004 708 0.004 961 1.761 6 1.992 0 
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