A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Grid</td><td align="center" colspan="2">Uniform</td><td align="center" colspan="2">Adaptive</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">Number of cells</td><td align="center">2500</td><td align="center">10000</td><td align="center">40000</td><td align="center">16562</td></tr><tr><td align="left"><svg height="11.6375" id="M254" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 20.525 11.6375" width="20.525" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.362)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g><g transform="matrix(.017,-0,0,-.017,10.959,11.362)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g>
</svg> (m)</td><td align="center">4.0</td><td align="center">2.0</td><td align="center">1.0</td><td align="center"> </td></tr><tr><td align="left">CPU time (s)</td><td align="center">0.375</td><td align="center">1.247</td><td align="center">6.621</td><td align="center">2.510</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Circular dam break: CPU time required by different simulations.

Mathematical Problems in Engineering

tab2

Table 2

Table 2: A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids 