<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
    <EXPANSIONS>
        <E COMPOSITE="C[1]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
        <E COMPOSITE="C[2]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
        <E COMPOSITE="C[3]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
    </EXPANSIONS>
    <CONDITIONS>
        <PARAMETERS>
            <P> FinTime         = 1.0               </P>
            <P> TimeStep        = 0.001             </P>
            <P> NumSteps        = FinTime/TimeStep  </P>
            <P> IO_CheckSteps   = 100               </P>
            <P> IO_InfoSteps    = 100               </P>
            <P> advx            = 2.0               </P>
            <P> advy            = 0.0               </P>
            <P> k               = 2*PI              </P>
        </PARAMETERS>
        
        <SOLVERINFO>
            <I PROPERTY="EQTYPE"                VALUE="UnsteadyAdvection"   />
            <I PROPERTY="Projection"            VALUE="DisContinuous"       />
            <I PROPERTY="AdvectionType"         VALUE="WeakDG"              />
            <I PROPERTY="UpwindType"            VALUE="Upwind"              />
            <I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
        </SOLVERINFO>
        
        <VARIABLES>
            <V ID="0"> u </V>
        </VARIABLES>
        
        <BOUNDARYREGIONS>
            <B ID="0"> C[100] </B>
            <B ID="1"> C[200] </B>
            <B ID="2"> C[300] </B>
            <B ID="3"> C[400] </B>
        </BOUNDARYREGIONS>
        
        <BOUNDARYCONDITIONS>
            <REGION REF="0">
                <D VAR="u" USERDEFINEDTYPE="TimeDependent"
                VALUE="sin(k*(x-advx*t))*cos(k*(y-advy*t))" />
            </REGION>
            <REGION REF="1">
                <P VAR="u" VALUE="[3]" />
            </REGION>
            <REGION REF="2">
                <D VAR="u" USERDEFINEDTYPE="TimeDependent"
                VALUE="sin(k*(x-advx*t))*cos(k*(y-advy*t))" />
            </REGION>
            <REGION REF="3">
                <P VAR="u" VALUE="[1]" />
            </REGION>
        </BOUNDARYCONDITIONS>
        
        <FUNCTION NAME="AdvectionVelocity">
            <E VAR="Vx" VALUE="advx" />
            <E VAR="Vy" VALUE="advy" />
        </FUNCTION>
        
        <FUNCTION NAME="ExactSolution">
            <E VAR="u"  VALUE="sin(k*(x-advx*t))*cos(k*(y-advy*t))" />
        </FUNCTION>
        
        <FUNCTION NAME="InitialConditions">
            <E VAR="u"  VALUE="sin(k*x)*cos(k*y)" />
        </FUNCTION>
    </CONDITIONS>
</NEKTAR>