<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>le</name>

  <author>Chaojie Mo</author>
  <description>
    The program solves the nonlinear lubrication equation. 
  </description>

  <features>
      <benchmark />
      <bing />
      <fftw plan="patient" />

      <auto_vectorise />
      <globals>
          <![CDATA[
          const double rho = 6;
          const double mu = 5;
          const double lambda = 7.2;
          const double R = 6.0;
          const double pi = 3.1415926;
          ]]>
       </globals>
     </features>

  <geometry>
      <propagation_dimension> t </propagation_dimension>
      <transverse_dimensions>
        <dimension name="z" lattice="120"  domain="(-30, 30)" transform="dft"/>
      </transverse_dimensions>
   </geometry>

  <vector name="hv" type="complex" dimensions="z">
    <components>h v</components>
    <initialisation>
      <![CDATA[
      h = R-0.01*R*cos(pi*z/60.0);
      v = 0;
      ]]>
    </initialisation>
  </vector>

  <sequence>
    <integrate algorithm="ARK89" interval="240.0" tolerance="1e-7">
      <samples>100</samples>
      <operators>
        <integration_vectors>hv</integration_vectors>
        <operator kind="ex">
          <operator_names>Lz</operator_names>
          <![CDATA[
            Lz = i*kz;
          ]]>
        </operator>

        <operator kind="ex">
          <operator_names>Lzzz</operator_names>
          <![CDATA[
            Lzzz = -i*kz*kz*kz;
          ]]>
        </operator>

        <operator kind="ex">
          <operator_names>Lzz</operator_names>
          <![CDATA[
            Lzz = -kz*kz;
          ]]>
        </operator>

 
        <![CDATA[
          dh_dt = -v*Lz[h] - h*Lz[v]/2.0;
          dv_dt = -v*Lz[v]  + 3.0*mu/rho/h/h*(2.0*h*Lz[h]*Lz[v]+h*h*Lzz[v]) - lambda/rho*((-Lz[h]*sqrt(1+Lz[h]*Lz[h]) - h*Lz[h]*Lzz[h]/sqrt(1+Lz[h]*Lz[h]))/(h*h*(1+Lz[h]*Lz[h])) - (Lzzz[h]*pow(1+Lz[h]*Lz[h],3.0/2.0)-3.0*Lz[h]*Lzz[h]*Lzz[h]*sqrt(1+Lz[h]*Lz[h]))/pow(1+Lz[h]*Lz[h],3.0));
        ]]>
 
      </operators>
    </integrate>
  </sequence>

  <output>
      <sampling_group basis="z" initial_sample="yes">
        <moments>hR hI vR vI</moments>
        <dependencies>hv</dependencies>
        <![CDATA[
          hR = h.Re();
          hI = h.Im();
          vR = v.Re();
          vI = v.Im();
        ]]>
      </sampling_group>
  </output>

</simulation>