1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method

<table>Idealized dam-break problem: (a) initial depth ratio <svg height="14.7" id="M88" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 68.087502 14.7" width="68.087502" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
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<text transform="matrix(1,0,0,-1,-56.97,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">𝐻</tspan>
</text>
<text transform="matrix(1,0,0,-1,-42.57,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑡</tspan>
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<text transform="matrix(1,0,0,-1,-35.86,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
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</svg>; (b) initial depth ratio <svg height="14.7" id="M89" style="vertical-align:-3.21404pt" version="1.1" viewbox="0 0 91.537498 14.7" width="91.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7)">
<g transform="translate(72,-60.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐻</tspan>
</text>
<text transform="matrix(1,0,0,-1,-61.03,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑟</tspan>
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<text transform="matrix(1,0,0,-1,-56.97,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">𝐻</tspan>
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<text transform="matrix(1,0,0,-1,-42.57,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑡</tspan>
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<text transform="matrix(1,0,0,-1,-35.86,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="24.530886" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="30.782387" y="0">0</tspan>
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Journal of Applied Mathematics

fig1

Figure 1

Figure 1: 1D and 2D Numerical Modeling for Solving Dam-Break Flow Problems Using Finite Volume Method 