Fig. 1. Slit problem, which is caused by the lack of interpolation points of the mirror points.狭缝问题(物体底部虚拟单元的镜像点缺乏合适的插值点)

Fig. 2. Demonstration of the improved ghost cell method.改进的虚拟单元法示意图

Fig. 3. Kink noted in the picture, which is happened when using the SGCM, and the comparison of the pressure coefficients obtained by using SGCM, MSGCM, ISGCM and the body fitted mesh.SGCM中出现的扭曲现象(标记区域)以及采用ISGCM求得的圆柱表面压力系数与采用SGCM、MSGCM、贴体网格得到的结果的对比

Fig. 4. The demonstration of the extended ISGCM.推广的改进型虚拟单元法示意图

Fig. 5. Physical model of the Schardin’s problem proposed by Chang et al.^[25]Chang等^[25]用来研究Schardin问题的物理模型

Fig. 6. Experimental results (left), Chang et al.^[25] results and the density contour computed by us (right): (a) T = 28 μs; (b) T = 53 μs; (c) T = 102 μs; (d) T = 130 μs; (e) T = 172 μs. 不同时刻下的实验结果(左)、Chang等^[25]计算所得的密度等值线(中)和采用ISGCM计算所得的密度等值线(右)　(a) T = 28 μs; (b) T = 53 μs; (c) T = 102 μs; (d) T = 130 μs; (e) T = 172 μs

Fig. 7. (a) Comparison of the density distribution along the symmetry plane between the results obtained by this paper and Chang et al.^[25] as well as the experiment; (b) the comparison of the Mach number distribution along the symmetry plane between the results obtained by this paper and the results of Chang et al.^[25]. (a)计算所得沿模型中间对称面上的密度分布与Chang等^[25]的计算结果以及实验数据的对比; (b)沿模型中间对称面上的马赫数分布与Chang等^[25]的计算结果的对比

Fig. 8. Physical model of the cylinder lift-off problem.激波抬升轻质圆柱问题的模型描述

Fig. 9. Pressure contour at T = 0.1641: (a) Extended ISGCM with the grid size of 600 × 120; (b) high-order ghost cell method proposed by Tan et al.^[8] with the grid size of 640 × 128. T = 0.1641时的压力等值线图　(a) 本文所推广的改进型虚拟单元法(网格量为600 × 120); (b) Tan等^[8]使用的高阶虚拟单元法(网格量为640 × 128)

Fig. 10. Pressure contour at T = 0.30085: (a) Extended ISGCM with the grid size of 600 × 120; (b) high-order ghost cell method proposed by Tan et al.^[8] with the grid size of 640 × 128. T = 0.30085时的压力等值线图　(a) 本文所推广的改进型虚拟单元法(网格量为600 × 120); (b) Tan等^[8]使用的高阶虚拟单元法(网格量为640 × 128)