Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method

<table>Stress overshoot at various <svg height="10.8125" id="M161" style="vertical-align:-0.20064pt" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜆</tspan>
</text>
</g>
</g>
</svg> when <svg height="10.9125" id="M162" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 59.012501 10.9125" width="59.012501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<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">R</tspan>
<tspan style="font-size: 12.50px; " x="8.3395014" y="0">e</tspan>
<tspan style="font-size: 12.50px; " x="19.442165" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="31.482553" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.734055" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="40.859802" y="0">0</tspan>
</text>
</g>
</g>
</svg> (a) along <svg height="10.9125" id="M163" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 45.424999 10.9125" width="45.424999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<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">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="26.856443" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="29.982195" y="0">0</tspan>
</text>
</g>
</g>
</svg> (b) along <svg height="11.0375" id="M164" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 61.049999 11.0375" width="61.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0375)">
<g transform="translate(72,-63.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="26.856443" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="29.982195" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="36.233692" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="42.485195" y="0">4</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Applied Mathematics

fig3

Figure 3

Figure 3: Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method 