我們在本文中提出了新的方法，以解兩相流介面的Eular五方程式模型。我們使用傳統的PPM方法加上BVD方法來調整處理後的介面及震波現象，在邊界處重建變量的不連續，從而有效地減少數值解的數值耗散。我們用該方法與原始的MUSCL法以及PPM法做比較，結果驗證本方法在捕獲多相流介面方面的能力，可以明確的處理多相流不連續的條件。因此我們提出的方法是一種簡單有效的模擬可壓縮多介面流的方法。

A new reconstruction scheme of cell state variables is presented to solve the five equation model for achieving high-resolution of interfaces and shock waves in two phase flows. We use a piecewise parabolic shock capturing scheme and the interface sharpening scheme as two building-blocks of spatial reconstruction to minimize the discontinuities of the reconstructed variables at cell boundaries, and thus the numerical dissipations is effectively reduced in numerical solutions. Benchmark test are shown to compare with original TVD scheme, to verify the ability of the present method in capturing the material interface as a well-defined sharp in volume fraction. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows.

Nomenclature	v
List of Figure	ix
1.	Introduction	1
1.1.	Background	1
1.2.	Numerical Algorithm Review	5
1.3.	Shock-Bubble Interaction Review	10
2.	Numerical Models	19
2.1.	Governing Equations	19
2.2.	Closures strategy	21
2.3.	Numerical Methodology	23
2.4.	Time Evolution	24
2.5.	HLLC Numerical Flux	25
2.6.	Interpolation Method	29
3.	Numerical Results	39
3.1.	Sod Problem	39
3.2.	Two Interacting Blast Waves Problem	41
3.3.	Grid Independence	45
3.4.	Two-Component Shock Tube Problem	46
3.5.	Two-Phase Gas-Liquid Shock Tube Problem	48
3.6.	R22 Gas Bubble	51
3.7.	Helium Bubble	54
4.	Conclusions	59
5.	References	61
Appendix	101
List of Figure
Figure 2.1 The solution of the HLLC scheme shows in the Star Region.	75
Figure 2.2 The intermediate fluxes shows in the Star Region.	75
Figure 3.1 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the Sod’s problem based on HLLC at time t = 0.25	76
Figure 3.2 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the Sod’s problem based on HLLC at time t = 0.25	77
Figure 3.3 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two interacting blast waves problem based on HLLC at time t = 0.38	78
Figure 3.4 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two interacting blast waves problem based on HLLC at time t = 0.38	79
Figure 3.5 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t = 0.38	80
Figure 3.6 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t =0.38	81
Figure 3.7 Numerical solutions of the density in the two interacting blast waves problem based on HLLC at time t =0.38	82
Figure 3.8 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-component shock tube problem based on HLLC at time t = 0.1	83
Figure 3.9 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-component shock tube problem based on HLLC at time t = 0.1	84
Figure 3.10 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-phase gas-liquid shock tube problem based on HLLC in gamma model at time t = 0.1	85
Figure 3.11 Numerical solutions of the (a) density, (b) velocity and (c) pressure in the two-phase gas-liquid shock tube problem based on HLLC in alpha model at time t = 0.1	86
Figure 3.12 Comparison between Schlieren plots and experiments. (a) t = 55 μs, (b) t = 115 μs, (c) t = 135 μs and (d) t = 187 μs	87
Figure 3.13 Comparison between Schlieren plots and experiments. (e) t = 247 μs, (g) t = 342 μs, (h) t = 417 μs and (i) t = 1020 μs	88
Figure 3.14 Comparison between Schlieren plots and experiments. (a) t = 55 μs, (b) t = 115 μs, (c) t = 135 μs and (d) t = 187 μs	89
Figure 3.15 Comparison between Schlieren plots and experiments. (e) t = 247 μs, (g) t = 342 μs, (h) t = 417 μs and (i) t = 1020 μs	90
Figure 3.16 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble	91
Figure 3.17 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble	92
Figure 3.18 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular R22 gas bubble	93
Figure 3.19 Comparison between Schlieren plots and experiments. (a) t = 32 μs, (b) t = 52 μs, (c) t = 62 μs and (d) t = 72 μs	94
Figure 3.20 Comparison between Schlieren plots and experiments. (f) t = 102 μs, (g) t = 245 μs, (h) t = 427 μs and (i) t = 67μs	95
Figure 3.21 Comparison between Schlieren plots and experiments. (a) t = 32 μs, (b) t = 52 μs, (c) t = 62 μs and (d) t = 72 μs	96
Figure 3.22 Comparison between Schlieren plots and experiments. (f) t = 102 μs, (g) t = 245 μs, (h) t = 427 μs and (i) t = 674 μs	97
Figure 3.23 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble	98
Figure 3.24 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble	99
Figure 3.25 Numerical results for a planar Mach 1.22 shock wave in air interacting with a circular helium-air bubble	100

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