A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center">Original-matrix</td><td align="center">Matrix-simplification</td><td align="center">Matrix-simplification with SOR</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">2nd order</td><td align="center">0.442 <svg height="14.85" id="M257" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M258" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M226 -163h-170v27q79 7 94 20t15 73v627q0 59 -15 72t-94 20v27h170v-866z" id="x5D"></path></g>
</svg></td><td align="center">0.423 <svg height="14.85" id="M259" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M260" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M226 -163h-170v27q79 7 94 20t15 73v627q0 59 -15 72t-94 20v27h170v-866z" id="x5D"></path></g>
</svg></td><td align="center">0.398 <svg height="14.85" id="M261" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M262" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M226 -163h-170v27q79 7 94 20t15 73v627q0 59 -15 72t-94 20v27h170v-866z" id="x5D"></path></g>
</svg></td></tr><tr><td align="left">3rd order</td><td align="center">2.925 <svg height="14.85" id="M263" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M264" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M226 -163h-170v27q79 7 94 20t15 73v627q0 59 -15 72t-94 20v27h170v-866z" id="x5D"></path></g>
</svg></td><td align="center">1.875 <svg height="14.85" id="M265" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M266" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M226 -163h-170v27q79 7 94 20t15 73v627q0 59 -15 72t-94 20v27h170v-866z" id="x5D"></path></g>
</svg></td><td align="center">1.662 <svg height="14.85" id="M267" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path d="M290 -163h-170v866h170v-28q-79 -7 -94 -19.5t-15 -72.5v-627q0 -59 14.5 -71.5t94.5 -19.5v-28z" id="x5B"></path></g>
</svg>s<svg height="14.85" id="M268" style="vertical-align:-1.95624pt" version="1.1" viewbox="0 0 5.9875002 14.85" width="5.9875002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

CPU time needed for advancing one time step for computing the turbulent boundary layer flow.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes 