Simulations in fluid flow
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Transcript of Simulations in fluid flow
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Simulation of 2014 Flood inPakistan
Ali Malik Ahmad
M1 Student
Hydraulic Research Lab
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Objectives
To simulate the precipitation in theKashmir Area using AdvectionEquation
To simulate the rise of water in TrimmuBarrage using Rate Equation
To simulate the flood in the suburban
areas of Trimmu using DiffusionEquation
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Trimmu Barrage
High Flood Level :490 Ft Design Capacity:600,000 Cusecs
Suburban districts:Multan, Muzafargarh,Toba Tek Singh, Khanewal,Jhang
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Precipitation
Rain Water moved from the KashmirRegionto the Punjab Region of Pakistan
Rain Fall : 511 mm recorded during 5 days
Advection Equation:FTCS Method (Central Difference Method)
Upwind Method
Lax Method
Lax-Wendroff Method
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Equations
FTCS Equation:ui
j+1= uij-u*dt/2dx(uji+1-u
ji-1)
Upwind Method Equation:
ui
j+1= ui
j-u*dt/dx(uji
-uji-1
), u>0
Lax Method:
uij+1= 1/2(uji+1+u
ji-1) -u*dt/2dx(u
ji+1-u
ji-1)
Lax Wondroff Equation:
fij+1
= b1fj
i1+b0fj
i +b1fj
i+1Where b1 =a/2*(a +1); b0= 1a2,b1=a/2*(a 1)
u 0.2m/s
dx 1000m
dt 3600sec
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Advection Equation:FTCS Method
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Advection Equation:FTCS Method
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Advection Equation:Lax Method
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Advection Equation:Lax Method
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Advection Equation:Upwind Method
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Advection Equation:Upwind Method
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Advection Equation:Upwind Method
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Advection Equation:Lax Wondroff
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Advection Equation:Lax Wondroff
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Conclusions:
FTCS method is unconditionally unstable Lax method gives stability to the FTCS
method(Dispersion Effect)
Upwind method is a conditionally stable method(u
