地震導致印度洋海嘯的波浪高度仿真

陸面體CFD工程師

本案例來自陸面體科技公眾號：

在中美貿易戰僵持的技術背景下，今天就不用美國的軟件來講這個案例了，我們來試試法國的開源軟件Gerris Flow Solver （以下簡稱Gerris）。Gerris由Stéphane Popinet創建，并由Institut Jean le Rond d'Alembert（該研究院屬于巴黎索邦大學）提供支持。現在Gerris的原始開發人員現在已經將開發轉移到了Basilisk，它可以完成Gerris可以做的大部分工作，甚至更多。

軟件主要特點如下：

- 求解時間依賴的不可壓縮變密度Euler，Stokes或Navier-Stokes方程

- 求解線性和非線性淺水波方程- 基于流場特征的網格自適應加密

- 復雜模型的網格自動化生成

- 空間和時間二階精度

- 不限數量的對流、擴散粒子追蹤- 可靈活加入源項

- MPI并行支持，動態負載平衡，并行可視化

- 基于VOF方法的多相流界面捕捉- 準確的表面張力模型

- 多相電-磁流體動力學

案例介紹

2004年印度洋海嘯是由于印度-澳大利亞和印度尼西亞的安達曼板塊邊界發生大規模斷層破裂（> 1000公里）造成的。該案例運用格里利等人的斷層模型作為圣維南原理分析海嘯的初始條件。圖1a中的動畫展示了波高的演變。追蹤波前中采用了自適應方法（圖1.b），地形的動態重建依據ETOPO1數據集。

(圖1a)波高動畫圖，圖中峰值大于2m小于 -2m；

(圖1b)自適應動畫圖，圖中波前峰值為海拔0.8海里和-101海里。

圖2展示了斷層破裂后在超過10小時的時間達到的最大波浪高度。

圖2：超過10小時后最大波浪高度云圖（以1m為顯示間隔）：

(a)孟加拉彎，最小值（藍色）0m，最大值（紅色）5m。

(b) 蘇門答臘北部和泰國附近的細節，最小值（藍色）0m，最大值（紅色）大于8m。

最后，圖3給出了在印度洋特定位置的不同時間觀測波高（使用潮汐測量儀）和模擬波高的對比圖。

圖3：在不同潮汐表位置觀測到的波高和模擬波高的對比。

備注：水平軸是斷層破裂后的時間（以小時為單位）。

圖4：觀測波高（Jason-1衛星測高儀）和模擬波高對比。

關鍵參數設置：

# Segment 1
Init {}
{
D = 0
}
InitOkada D
{
x = 94.57
y = 3.83
depth = 11.4857e3
strike = 323
dip = 12
rake = 90
length = 220e3
width = 130e3
U = 18
}
# Initial water level is at z = D
Init
{
start = 0
}
{
P = MAX (0., D - Zb)
}

# Segment 2
EventList
{
start = 212
step = 6
end = 272
}
{
Init {}
{
D = 0
}
InitOkada D
{
x = 93.90
y = 5.22
depth = 11.4857e3
strike = 348
dip = 12
rake = 90
length = 150e3
width = 130e3
U = 23
}
}
# make sure the deformation is well resolved
AdaptGradient
{
start = 212
istep = 1
end = 272
}
{
cmax = 0.05
cfactor = 2
minlevel = 5
maxlevel = LEVEL
} D
# add it to the current elevation field (only if wet)
Init
{
start = 272
}
{
P = (P < DRY ? P : MAX (0., P + D))
}

# Segment 3
EventList
{
start = 528
step = 6
end = 588
}
{
Init {}
{
D = 0
}
InitOkada D
{
x = 93.21
y = 7.41
depth = 12.525e3
strike = 338
dip = 12
rake = 90
length = 390e3
width = 120e3
U = 12
}
}
# make sure the deformation is well resolved
AdaptGradient
{
start = 528
istep = 1
end = 588
}
{
cmax = 0.05
cfactor = 2
minlevel = 5
maxlevel = LEVEL
} D
# add it to the current elevation field (only if wet)
Init
{
start = 588
}
{
P = (P < DRY ? P : MAX (0., P + D))
}

# Segment 4
EventList
{
start = 853
step = 6
end = 913
}
{
Init {}
{
D = 0
}
InitOkada D
{
x = 92.60
y = 9.70
depth = 15.12419e3
strike = 356
dip = 12
rake = 90
length = 150e3
width = 95e3
U = 12
}
}
# make sure the deformation is well resolved
AdaptGradient
{
start = 853
istep = 1
end = 913
}
{
cmax = 0.05
cfactor = 2
minlevel = 5
maxlevel = LEVEL
} D
# add it to the current elevation field (only if wet)
Init
{
start = 913
}
{
P = (P < DRY ? P : MAX (0., P + D))
}

# Segment 5
EventList
{
start = 1213
step = 6
end = 1273
}
{
Init {}
{
D = 0
}
InitOkada D
{
x = 92.87
y = 11.70
depth = 15.12419e3
strike = 10
dip = 12
rake = 90
length = 350e3
width = 95e3
U = 12
}
}

參考資料

[1] Hyunuk An and Soonyoung Yu. Well-balanced shallow water flow simulation on quadtree cut cell grids. Advances in Water Resources, 39:60–70, 2012.
[2] H. Glauert. The Elements of Aerofoil and Airscrew Theory. Cambridge University Press, 1926.
[3] S.T. Grilli, M. Ioualalen, J. Asavanant, F. Shi, J.T. Kirby, and P. Watts. Source constraints and model simulation of the December 26, 2004, Indian Ocean Tsunami. Journal of Waterway, Port, Coastal, and Ocean Engineering, 133:414–428, 2007.
[4] N.R. Hanson. A picture theory of theory meaning. The nature and function of scientific theories, pages 233–274, 1970.
[5] E. N. Jacobs, K. E. Ward, and R. M. Pinkerton. The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel. Technical report, NACA Technical Report 460, 1933.
[6] P.-Y. Lagrée, L. Staron, and S. Popinet. The granular column collapse as a continuum: validity of a Navier–Stokes model with a μ(i)-rheology. Journal of Fluid Mechanics, 2011.
[7] R.J. LeVeque and D.L. George. High-resolution finite volume methods for the shallow water equations with bathymetry and dry states. Advanced numerical models for simulating tsunami waves and runup, 10:43–73, 2006.
[8] L.M. Milne-Thomson. Theoretical aerodynamics (4th ed.). Dover, New York, 1973.
[9] S. Popinet. Quadtree-adaptive tsunami modelling. Ocean Dynamics, 61(9):1261–1285, 2011.
[10] C. Rosales and C. Meneveau. Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties. Physics of Fluids, 17:095106, 2005.
[11] L. Staron and E. J. Hinch. Study of the collapse of granular columns using two-dimensional discrete-grain simulation. Journal of Fluid Mechanics, 545:1–27, 2005.
[12] J. J. Videler. Avian Flight. Oxford Ornithological Studies. Oxford University Press, 2006.