cnoidalFirst::cnoidalFirst
(
const word & subDictName,
const fvMesh & mesh_
)
:
waveTheory(subDictName, mesh_),
H_(readScalar(coeffDict_.lookup("height"))),
h_(readScalar(coeffDict_.lookup("depth"))),
omega_(readScalar(coeffDict_.lookup("omega"))),
propagationDirection_(vector(coeffDict_.lookup("direction"))),
m_(readScalar(coeffDict_.lookup("m"))),
length_(readScalar(coeffDict_.lookup("length"))),
celerity_(readScalar(coeffDict_.lookup("celerity")))
{
scalar Eelliptic = gsl_sf_ellint_Ecomp( Foam::sqrt(m_), GSL_PREC_DOUBLE);
period_ = 2.0 * PI_ / omega_;
Kelliptic_ = gsl_sf_ellint_Kcomp( Foam::sqrt(m_), GSL_PREC_DOUBLE);
etaMin_ = ((1.0 - Eelliptic / Kelliptic_) / m_ - 1.0) * H_;
propagationDirection_ /= Foam::mag(propagationDirection_);
Tsoft_ = coeffDict_.lookupOrDefault<scalar>("Tsoft",period_);
}
void cnoidalFirstProperties::set( Ostream& os)
{
scalar m = solve();
// Write the beginning of the sub-dictionary
writeBeginning( os );
// Write the already given parameters
writeGiven( os, "waveType" );
if (dict_.found( "Tsoft" ))
{
writeGiven( os, "Tsoft");
}
writeGiven( os, "depth");
writeGiven( os, "period");
writeGiven( os, "height");
if (m < 0.0)
{
Info << "\nPARAMETERS NOT SET\nNo cnoidal wave solution"
<< " exists for given input\n" << endl;
}
else
{
double K = gsl_sf_ellint_Kcomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double E = gsl_sf_ellint_Ecomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double A = 2.0/m - 1.0 - 3.0/m*E/K;
double L =
Foam::sqrt(16.0*m * Foam::pow(K, 2.0)*Foam::pow(d_, 3.0)/(3.0*H_));
double c = Foam::sqrt( G_*d_*(1 + A*H_/d_));
double omega = 2*PI_/T_;
if (write_)
{
writeDerived(os, "omega", omega);
writeDerived(os, "length", L);
writeDerived(os, "celerity", c);
// Locally change the write precision for m to avoid it being
// written as 1 instead of 0.9999999999 which makes elliptic
// integrals to infinity.
unsigned int pre = os.precision( 14 );
writeDerived(os, "m", m);
os.precision( pre );
}
}
writeGiven( os, "direction" );
// Write the relaxation zone
writeRelaxationZone( os );
// Write the closing bracket
writeEnding( os );
}
double
ell (double x)
{
double k = x;
gsl_mode_t mode = GSL_PREC_DOUBLE;
double var = (gsl_sf_ellint_Kcomp(k, mode) - gsl_sf_ellint_Ecomp(k, mode));
return var;
}
double lowerMBound_f ( double m, void *params )
{
// Solves to find the value of m at which Foam::sqrt(1.0 + H/d*A) == 0.0
struct cnoidalFirstParams *p = (struct cnoidalFirstParams * ) params;
double d = p->depth_;
double H = p->height_;
double K = gsl_sf_ellint_Kcomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double E = gsl_sf_ellint_Ecomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double A = 2.0/m - 1.0 - 3.0/m*E/K;
// The value of 1.0e-8 is added to ensure strictly larger than 0!
return 1.0 - 1.0e-8 + H/d*A;
}
double cnoidalFirst_f ( double m, void *params)
{
struct cnoidalFirstParams *p = (struct cnoidalFirstParams * ) params;
double T = p->period_;
double d = p->depth_;
double G = p->g_;
double H = p->height_;
double K = gsl_sf_ellint_Kcomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double E = gsl_sf_ellint_Ecomp( Foam::sqrt(m), GSL_PREC_DOUBLE );
double A = 2.0/m - 1.0 - 3.0/m*E/K;
return T*Foam::sqrt(G/d)*Foam::sqrt(1.0 + H/d*A)
- Foam::sqrt( 16.0*d/(3.0*H)*m * Foam::pow(K, 2.0) );
}
/**
* C++ version of gsl_sf_ellint_Kcomp().
* Legendre form of complete elliptic integrals
*
* K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]
*
* @param k A real number
* @param mode The mode
* @return function value
*/
inline double Kcomp( double k, mode_t mode ){
return gsl_sf_ellint_Kcomp( k, mode ); }
inline double set_vs( int is, int ns, double kprime ){
double ekprime = gsl_sf_ellint_Kcomp( kprime , 0 );
double vs = is * ekprime / ns;
return vs;
}
