A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

<table>Numerical solutions for <svg height="10.9125" id="M135" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 62.525002 10.9125" width="62.525002" xmlns="http://www.w3.org/2000/svg">
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<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜈</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.408978" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="43.660477" y="0">1</tspan>
</text>
</g>
</g>
</svg>, at different times with <svg height="12.8875" id="M136" style="vertical-align:-1.76814pt" version="1.1" viewbox="0 0 118.5125 12.8875" width="118.5125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.8875)">
<g transform="translate(72,-61.69)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="6.6515961" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="16.991577" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="29.031965" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="35.283466" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="38.409218" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="44.660717" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="50.912216" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="57.163715" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="66.540962" y="0">𝜏</tspan>
<tspan style="font-size: 12.50px; " x="76.418335" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="88.458725" y="0">1</tspan>
</text>
</g>
</g>
</svg> and <svg height="11.1" id="M137" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 75.699997 11.1" width="75.699997" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="6.6515961" y="0">𝑡</tspan>
<tspan style="font-size: 12.50px; " x="14.028366" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.068754" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="32.320255" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="35.446007" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="41.697506" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="47.949005" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="54.200504" y="0">5</tspan>
</text>
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Journal of Applied Mathematics

fig3

Figure 3

Figure 3: A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method 