本論文利用CE/SE對於震波通過半菱形與楔形塊現象的探討，而且在本論文中我們也發現CE/SE的高準確度與低數值耗散的優點。此外利用CE/SE可以求得暫態解的特性，來幫助我們對於震波繞射現象的了解。並且我們利用這些暫態過程與Glass在1987年的實驗作一比較，我們可以發現除了因為黏滯效應所產生的結構之外，其他結構方面則有非常好的相似結果。
在本數值模擬過程中，我們也將渦量與環流量一併考慮進來。因此藉由渦量分佈圖可以清楚的了解到由速度差異所產生的剪力層，並且更進一步的得到剪力層、主渦漩以及二次反射波(由繞射波與後板所產生的結構)之交互作用。我們也發現，當入射波馬赫數越大的時候，滑移線與接觸面(contact surface)的交互作用也會越明顯，並且對於繞射之後的流場結構也會趨於複雜。
另外，環流量會因為二次反射波與楔形塊的頂點角度而有所改變。當繞射角度越大，所得到的環流量就會越多。此外，二次反射會先與靠近壁面的接觸面作用，再與主渦漩作用，此時二次反射會因此而分成兩段，這將會產生更複雜的流場結構型態。

The diffraction of planer shock waves over a wedge has been investigated in this study by the conservation element and solution element method. We found that the CE/SE method has high numerical accuracy and low numerical dispersion. The method is very convenient to obtain the transient solution so as to comprehend the shock diffraction. We also compare this simulation result with experiment which has been studied by Glass in 1987 and the shock structure is almost identical to what we obtained except the viscous effect.
In this simulation, we quantified the vorticity and circulation. The shear layer caused by the velocity difference can be clearly understood with the help of the voricity contour. Furthermore, we study the interaction among the shear layer, main vortex and secondary reflected shock which is the diffracted shock interacting with the backward flat surface. We also found that with the increase of the incident shock’s Mach number, the interaction between contact surface and slipstream will be stronger. And the flow structure after the shock diffraction is more complicated if increasing the Mach number of the incident shock.
In this study, the results show that the circulation is influenced by both the secondary reflected shock and the wedge angle. The circulation increases as the backward wedge angle increases. The secondary reflected shock interacts with the contact surface first and then with the main vortex. This causes the secondary shock break into two parts and makes the flow structure more complicated.

[1] B.W. Skews,”The perturbed region behind a diffracting shock wave”, J. Fluid
Mech., 1967, vol.29, par4, pp.705-720.
[2] R.Hillier,”Computation of shock wave diffraction at a ninety degrees convex
edge”, Shock Waves, pp.89-98.
[3] K.Takayama, O.Inoue,”Shock diffraction over a 90 degree sharp corner
–Posters presented at 18the Issw-”, Shock Waves, 1991, pp.301-312
[4] M.Sun, K.Takayama,”A note on numerical simulation of vertical structures in
shock diffraction”, Shock Waves, 2003.
[5] M.Sun, K.Takayama,”Vorticity production in shock diffraction”, J. Fluid
Mech., 2003, vol478, pp.237-256.
[6] D.L.Zhang, I.I.Glass,”An interferometric investigation of the diffraction of
planar shock waves over a half-diamond cylinder in air”, UTIAS Report no.322,
1987.
[7] I.I.Glass, J.Kaca, D.L.Zhang, H.M.Glaz, J.B.Bell, J.A.Trangenstein, J.P.
Collins,”Diffraction of planar shock waves over half-diamond and semicircular
cylinder: an experiment and numerical comparison”, AIP conference proceedings
208, 1989, pp.246-251.
[8] I.I.Glass, J.P.Sislian, Nonstationary Flows and Shock Waves，Oxford, 1994,
pp.273-249.
[9] D.Kh.Ofengeim, D.Drikakis,”Simulation of the blast wave propagation over a
cylinder”, Shock Waves, 1997, pp.305-317.
[10] D.Drikakis, D.Ofengeim,”Computation of non-stationary shock-wave/cylinder
interaction using adaptive-grid methods”, Journal of Fluids and Structures,
1997(11), pp.665-691.
[11] J.Zoltak, D.Drikakis,”Hybrid upwind methods for the simulation of unsteady
shock-wave diffraction over a cylinder”, Comput. Methods Appl. Mech.
Engerg., 1998(162), pp.165-185.
[12] S.Sivier, E.Loth, J.Baum, R.Lohoner,”Vorticity produced by shock wave
diffraction”, Shock Waves, 1992(2), pp.31-41.
[13] O.Igra, J.Falcovitz, H.Reichenbach , W.Heilig, ”Experimental and numerical
study of the interaction between a planar shock wave and a square cavity”,
1996, vol.313, pp.105-130.
[14] B.W.Skews,”The shape of a diffraction shock wave ”, J. Fluid Mech., 1967,
vol.29, part2, pp.297-304.
[15] T.H.Yi, G.Emaniel, ”Unsteady shock generated vorticity”, Shock Waves,
2000(10), pp.179-184.
[16] H.Li., G.Ben-Dor, ”Analysis of double-Mach-Reflection wave configurations
with convexly curved Mach stems”, Shock Waves, 1999(9), 319-326.
[17] G.Ben-Dor,”Shock Wave Reflection Phenomena”, Springer-Verlag, 1992,
pp.39-59.
[18] S.C.Chang,”The method of space-time conservation element and solution
element—a new approach for solving the Navier-Stokes and Euler equation”,
J. Comput. Phys., 1995(119), pp.295-324.
[19] Z.C.Zhang, S.T.John Yu, S.C.Chang,”A space-time conservation element and
solution element methods for solving the two-and three-dimensional unsteady
Euler equations using quadrilateral and hexahedral meshes”, J. Comput.
Phys., 2002(175), pp.168-199.
[20] Z.Y.Han, X.Z.Yin,”Shock dynamics”, Kluwer Academic Publishers, 1993,
pp.50-60.
[21] C.K.Kim, K.S.Im, S.-T.John Yu,”Direct calculation of high-speed cavity flows
in a scramjet engine by the CESE method”, AIAA meeting paper, 2000.
[22] Y.Takakura, F.Higashino,”Self-sustained oscillations caused by interacting
phenomena in supersonic cavity flows”, Proceedings of the third
international workshop on shock wave- vortex interaction, 1999 Sep. 12-14,
pp.63-86.
[23] 楊自森，”弱震波於楔型體上反射-繞射現象之探討”，國立成功大學航太研究所碩士論
文，1997.