Comparison between 1D and 2D models to analyze the dam break
Comparison between 1D and 2D models to analyze the dam break
Comparison between 1D and 2D models to analyze the dam break
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<strong>Comparison</strong> <strong>between</strong> <strong>1D</strong> <strong>and</strong> <strong>2D</strong> <strong>models</strong> <strong>to</strong> <strong>analyze</strong> <strong>the</strong> <strong>dam</strong> <strong>break</strong> waveIn <strong>1D</strong>, Comsol Multiphysics always uses regularrefinement, where it divides each element in<strong>to</strong> twoelements of <strong>the</strong> same shape. The refinement of <strong>the</strong>mesh has gone from 15 <strong>to</strong> 7680 elements, <strong>the</strong> finaldivision that has been chosen <strong>to</strong> define <strong>the</strong> model withan acceptable accuracy.Figure 8. The initial condition specification page in <strong>the</strong>Subdomain Settings dialog box.3.8 Meshing.A mesh is a partition of <strong>the</strong> geometric model in<strong>to</strong>small units of simple shape. For <strong>1D</strong> geometry <strong>the</strong>software partitions <strong>the</strong> subdomains (intervals) in<strong>to</strong>smaller intervals (or mesh elements). The endpoints of<strong>the</strong> mesh elements are called ‘mesh vertices’.The value in <strong>the</strong> ‘Maximum element size’ edit fieldspecifies <strong>the</strong> maximum allowed element size, which bydefault is 1/15th of <strong>the</strong> size of <strong>the</strong> geometry.The value in <strong>the</strong> ‘Maximum element size scalingfac<strong>to</strong>r’ edit field comes in<strong>to</strong> play if we do not explicitlygive a maximum element size. In that case, <strong>the</strong>software multiplies <strong>the</strong> default maximum element sizeby this fac<strong>to</strong>r; its default value is 1.The value in <strong>the</strong> ‘Element growth rate’ edit fielddetermines <strong>the</strong> maximum rate at which <strong>the</strong> elementsize can grow from a region with small elements <strong>to</strong> aregion with larger elements. The value must be greateror equal <strong>to</strong> one. The default value is 1.3, that is,element size can grow by 30% (approximately) fromone element <strong>to</strong> ano<strong>the</strong>r.Table 2. Mesh parameters <strong>and</strong> statistics.ParameterMaximum element size 1Maximum element size scaling fac<strong>to</strong>r 1ValueElement growth rate 1.3X-direction scale fac<strong>to</strong>r 1.0Number of degrees of freedom 30722Number of elements 76803.9 Subdomain settings.The subdomain settings describe <strong>the</strong> physics on amodel’s main domain, which is divided in<strong>to</strong>subdomains. In this model, <strong>the</strong>re is only onesubdomain.The PDE in its general form is used with a timedependent analysis. The PDE in <strong>the</strong> general form has<strong>the</strong> following aspect in <strong>the</strong> program:e2∂ u+ d∂t∂u⋅ + ∇ ⋅ Γ∂ta⋅a=2F(11)The next step is <strong>to</strong> introduce <strong>the</strong> equations seen in[2.2] adapting <strong>the</strong>m <strong>to</strong> this general form, that is, <strong>the</strong><strong>1D</strong>-SWE must be introduced in <strong>the</strong> proper formatthat Comsol Multiphysics requires.Figure 9. The flux vec<strong>to</strong>r edit fieldWhen trying <strong>to</strong> solve a problem that does notconverge, or having solved a problem where <strong>the</strong>solution does not seem properly resolved, <strong>the</strong>re isoften a need for re-solving <strong>the</strong> problem using a finermesh. In <strong>the</strong>se situations it is sometimes easier <strong>to</strong>refine <strong>the</strong> existing mesh than <strong>to</strong> regenerate <strong>the</strong> meshfrom scratch using finer mesh settings.Figure 10. The source term edit field9