An Alternative Scheme to Calculate the Strain Rate Tensor for the LES Applications in the LBM

<table>Results for <svg height="9.7875004" id="M170" style="vertical-align:-0.1575pt" version="1.1" viewbox="0 0 63.424999 9.7875004" width="63.424999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.7875)">
<g transform="translate(72,-64.17)">
<text transform="matrix(1,0,0,-1,-71.95,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">R</tspan>
<tspan style="font-size: 11.21px; " x="7.4757361" y="0">e</tspan>
<tspan style="font-size: 11.21px; " x="17.42844" y="0">=</tspan>
<tspan style="font-size: 11.21px; " x="28.221745" y="0">1</tspan>
<tspan style="font-size: 11.21px; " x="33.825745" y="0">0</tspan>
<tspan style="font-size: 11.21px; " x="39.429745" y="0">0</tspan>
<tspan style="font-size: 11.21px; " x="45.033745" y="0">0</tspan>
</text>
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</svg> at the 200th time step, traditional scheme: solid line, current scheme: dashed line, <svg height="13.2" id="M171" style="vertical-align:-2.89917pt" version="1.1" viewbox="0 0 56.362499 13.2" width="56.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.2)">
<g transform="translate(72,-61.44)">
<text transform="matrix(1,0,0,-1,-71.95,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">𝐶</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.43,61.57)">
<tspan style="font-size: 7.85px; " x="0" y="0">𝑠</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.37,64.37)">
<tspan style="font-size: 11.21px; " x="0" y="0">=</tspan>
<tspan style="font-size: 11.21px; " x="10.793304" y="0">0</tspan>
<tspan style="font-size: 11.21px; " x="16.397305" y="0">.</tspan>
<tspan style="font-size: 11.21px; " x="19.199305" y="0">1</tspan>
<tspan style="font-size: 11.21px; " x="24.803305" y="0">7</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: An Alternative Scheme to Calculate the Strain Rate Tensor for the LES Applications in the LBM 