helperFunc Namespace Reference

Classes
class	KAndDisp
	return type specifically for fuctions returning k and disp at once More...
class	KAndDispAndKtAndDispt
	return type specifically for fuctions returning k, disp, kt, dispt at once More...

Functions
KAndDisp	computeKAndDispFromCollisionTimeAndRestitutionCoefficientAndEffectiveMass (Mdouble tc, Mdouble r, Mdouble mass)
	Set disp and k such that is matches a given collision time tc and restitution coefficient r for a collision of effective/reduced mass m. More...
KAndDispAndKtAndDispt	computeDisptFromCollisionTimeAndRestitutionCoefficientAndTangentialRestitutionCoefficientAndEffectiveMass (Mdouble tc, Mdouble r, Mdouble beta, Mdouble mass)
	Set disp, k, dispt and kt such that is matches a given collision time tc and a normal andtangential restitution coefficient r, beta for a collision of effective/reduced mass m. More...
Mdouble	getCollisionTime (Mdouble k, Mdouble disp, Mdouble mass)
	Calculates collision time for two copies of a particle of given disp, k, effective mass. More...
Mdouble	getRestitutionCoefficient (Mdouble k, Mdouble disp, Mdouble mass)
	Calculates restitution coefficient for two copies of given disp, k, effective mass. More...
Mdouble	getMaximumVelocity (Mdouble k, Mdouble disp, Mdouble radius, Mdouble mass)
	Calculates the maximum relative velocity allowed for a normal collision of two particles of radius r and particle mass m (for higher velocities particles could pass through each other) More...

Function Documentation

helperFunc::KAndDispAndKtAndDispt helperFunc::computeDisptFromCollisionTimeAndRestitutionCoefficientAndTangentialRestitutionCoefficientAndEffectiveMass	(	Mdouble	tc,
		Mdouble	r,
		Mdouble	beta,
		Mdouble	mass
	)

Set disp, k, dispt and kt such that is matches a given collision time tc and a normal andtangential restitution coefficient r, beta for a collision of effective/reduced mass m.

from Deen...Kuipers2006, eq. 43 and 30

From Deen...Kuipers2006, eq. 43 and 30

Definition at line 221 of file ExtendedMath.cc.

References helperFunc::KAndDispAndKtAndDispt::disp, helperFunc::KAndDispAndKtAndDispt::dispt, helperFunc::KAndDispAndKtAndDispt::k, helperFunc::KAndDispAndKtAndDispt::kt, constants::pi, and sqr.

{
    helperFunc::KAndDispAndKtAndDispt ans;
    ans.disp = - 2.0 * mass * log(r) / tc;
    ans.k  = mass * (sqr(constants::pi/tc) + sqr(ans.disp/(2.0*mass)));
    ans.kt = 2.0/7.0*ans.k*(sqr(constants::pi)+sqr(log(beta)))/(sqr(constants::pi)+sqr(log(r)));
    if (beta!=0.0) ans.dispt = -2*log(beta)*sqrt(1.0/7.0*mass*ans.kt/(sqr(constants::pi)+sqr(log(beta))));
    else ans.dispt = 2.*sqrt(1.0/7.0*mass*ans.kt);
    return ans;
}   

helperFunc::KAndDisp helperFunc::computeKAndDispFromCollisionTimeAndRestitutionCoefficientAndEffectiveMass	(	Mdouble	tc,
		Mdouble	r,
		Mdouble	mass
	)

Set disp and k such that is matches a given collision time tc and restitution coefficient r for a collision of effective/reduced mass m.

Definition at line 212 of file ExtendedMath.cc.

References helperFunc::KAndDisp::disp, helperFunc::KAndDisp::k, constants::pi, and sqr.

{
    helperFunc::KAndDisp ans;
    ans.disp = - 2.0 * mass * std::log(r) / tc;
    ans.k = mass * (sqr(constants::pi/tc) + sqr(ans.disp/(2.0*mass)));
    return ans;
}   

Mdouble helperFunc::getCollisionTime	(	Mdouble	k,
		Mdouble	disp,
		Mdouble	mass
	)

Calculates collision time for two copies of a particle of given disp, k, effective mass.

Definition at line 232 of file ExtendedMath.cc.

References constants::pi, and sqr.

Referenced by getRestitutionCoefficient().

{
    
    //check for errors in input
    if(mass<=0)     
    {
        std::cerr << "Error in get_collision_time(Mdouble mass) mass is not set or has an unexpected value, (get_collision_time("<<mass<<"))"<< std::endl; 
        exit(-1);
    }
    if(k<=0)        
    {
        std::cerr << "Error in get_collision_time(Mdouble mass) stiffness is not set or has an unexpected value, (get_collision_time("<<mass<<"), with stiffness="<<k<<")"<< std::endl; 
        exit(-1);
    }
    if(disp<0)      
    {
        std::cerr << "Error in get_collision_time(Mdouble mass) dissipation is not set or has an unexpected value, (get_collision_time("<<mass<<"), with dissipation="<<disp<<")"<< std::endl; 
        exit(-1);
    }
    
    //calculate square of oscillation frequency
    Mdouble w2=k/mass - sqr(disp/(2.0*mass));
    
    if (w2<=0)  
    {
        std::cerr << "Error in get_collision_time(Mdouble mass) values for mass, stiffness and dissipation lead to an over-damped system, (get_collision_time("<<mass<<"), with stiffness="<<k<<" and dissipation="<<disp<<")"<< std::endl; 
        exit(-1);
    }
    
    return constants::pi / sqrt( w2 );
}

Mdouble helperFunc::getMaximumVelocity	(	Mdouble	k,
		Mdouble	disp,
		Mdouble	radius,
		Mdouble	mass
	)

Calculates the maximum relative velocity allowed for a normal collision of two particles of radius r and particle mass m (for higher velocities particles could pass through each other)

Definition at line 269 of file ExtendedMath.cc.

References sqr.

{
    // note: underestimate based on energy argument,
    // Ekin = 2*1/2*m*(v/2)^2 = 1/2*k*(2*r)^2, gives
    // return radius * sqrt(8.0*k/mass);

    // with dissipation, see S. Luding, Collisions & Contacts between two particles, eq 34
    Mdouble w = sqrt(k/mass - sqr(disp/(2.0*mass)));
    Mdouble w0 = sqrt(k/mass);
    Mdouble DispCorrection = exp(-disp/mass/w)*asin(w/w0);
    //std::cout << "DispCorrection" << DispCorrection << std::endl;
    return radius * sqrt(8.0*k/mass) / DispCorrection;
}

Mdouble helperFunc::getRestitutionCoefficient	(	Mdouble	k,
		Mdouble	disp,
		Mdouble	mass
	)

Calculates restitution coefficient for two copies of given disp, k, effective mass.

Definition at line 264 of file ExtendedMath.cc.

References getCollisionTime().

{
    return exp(-disp/(2.0*mass)*helperFunc::getCollisionTime(k, disp, mass));
}