advection.xmds

<?xml version="1.0"?>
<simulation>

  <!-- Global system parameters and functionality -->
  <name> advection </name>      <!-- the name of the simulation -->
  <author> Paul Cochrane </author>  <!-- the author of the simulation -->
  <description>
    Solves the one-dimensional advection equation for an initial 
    cosine-modulated Gaussian pulse.  
    Adapted from A. L. Garcia, "Numerical Methods in Physics" (1994).
  </description>

  <prop_dim> t </prop_dim>    <!-- name of main propagation dim -->

  <error_check> yes </error_check>   <!-- defaults to yes -->
  <use_wisdom> yes </use_wisdom>     <!-- defaults to no -->
  <benchmark> yes </benchmark>       <!-- defaults to no -->

  <!-- Command line arguments -->
  <argv>
    <arg>
      <name> v </name>
      <type> double </type>
      <default_value> 1.0 </default_value>
    </arg>
    <arg>
      <name> x0 </name>
      <type> double </type>
      <default_value> 0.0 </default_value>
    </arg>
    <arg>
      <name> sigma </name>
      <type> double </type>
      <default_value> 0.1 </default_value>
    </arg>
  </argv>

  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
      //const double v = 1.0;
      //const double x0 = 0.0;
      //const double sigma = 0.1;
      double k = M_PI/sigma;
  ]]>
  </globals>

  <!-- Field to be integrated over -->
  <field>
    <name> main </name>
    <dimensions> x </dimensions> <!-- transverse dims -->
    <lattice> 50 </lattice>       <!-- no. pts for each dim -->
    <domains> (-0.5,0.5) </domains> <!-- domain of each dim -->
    <samples> 1 </samples>       <!-- sample 1st point of dim? -->
    
    <vector>
      <name> main </name>
      <type> complex </type>          <!-- data type of vector -->
      <components> A </components>    <!-- names of components -->
      <fourier_space> no </fourier_space> <!-- def in k-space? -->
      <![CDATA[
	  A = rcomplex(
	      cos(k*(x-x0)) * exp(-(x-x0)*(x-x0)/(2.0*sigma*sigma))
	        , 0.0);
      ]]>
    </vector>
  </field>

  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm> RK4EX </algorithm> <!-- RK4EX, RK4IP, SIEX, SIIP -->
      <interval> 1 </interval>   <!-- how far in main dim? -->
      <lattice> 500 </lattice>     <!-- no. points in main dim -->
      <samples> 50 </samples> <!-- no. pts in output moment group -->
      
      <k_operators>
        <constant> yes </constant>         <!-- yes/no -->
	<operator_names> L </operator_names>
	<![CDATA[
	    L = rcomplex(0.0, -v*kx);
	]]>
      </k_operators>
      
      <![CDATA[
	  dA_dt = L[A];
      ]]>
    </integrate>
  </sequence>

  <!-- The output to generate -->
  <output format="ascii">
    <group>
      <sampling>
        <fourier_space> no </fourier_space> <!-- sample in k-space? -->
	<lattice> 50 </lattice>           <!-- no. points to sample -->
	<moments> amp </moments>           <!-- names of moments -->
	<![CDATA[
	    amp = A;
	]]>
      </sampling>
    </group>
  </output>

</simulation>