dg::geo::SimpleOrthogonal Struct Reference

Generate a simple orthogonal grid. More...

Inheritance diagram for dg::geo::SimpleOrthogonal:

Public Member Functions
	SimpleOrthogonal (const CylindricalFunctorsLvl2 &psi, double psi_0, double psi_1, double x0, double y0, double psi_firstline, int mode=0)
	Construct a simple orthogonal grid. More...
	SimpleOrthogonal (const CylindricalFunctorsLvl2 &psi, const CylindricalSymmTensorLvl1 &chi, double psi_0, double psi_1, double x0, double y0, double psi_firstline, int mode=0)
	Construct a simple orthogonal grid. More...
double	f0 () const
	The grid constant. More...
virtual SimpleOrthogonal *	clone () const override final
	Abstract clone method that returns a copy on the heap. More...
Public Member Functions inherited from dg::geo::aRealGenerator2d< real_type >
real_type	width () const
	length in \( \zeta\) of the computational space More...
real_type	height () const
	length in \( \eta\) of the computational space More...
bool	isOrthogonal () const
	sparsity pattern for metric More...
void	generate (const thrust::host_vector< real_type > &zeta1d, const thrust::host_vector< real_type > &eta1d, thrust::host_vector< real_type > &x, thrust::host_vector< real_type > &y, thrust::host_vector< real_type > &zetaX, thrust::host_vector< real_type > &zetaY, thrust::host_vector< real_type > &etaX, thrust::host_vector< real_type > &etaY) const
	Generate grid points and elements of the Jacobian. More...
virtual aRealGenerator2d *	clone () const =0
	Abstract clone method that returns a copy on the heap. More...
virtual	~aRealGenerator2d ()

Additional Inherited Members
Protected Member Functions inherited from dg::geo::aRealGenerator2d< real_type >
	aRealGenerator2d ()
	empty More...
	aRealGenerator2d (const aRealGenerator2d &)
	empty More...
aRealGenerator2d &	operator= (const aRealGenerator2d &)
	return *this More...

Detailed Description

Generate a simple orthogonal grid.

First discretize a closed flux surface. Then each point is followed along the gradient of Psi to obtain the points on other flux surfaces.

Note

find more details in M. Wiesenberger, M. Held, L. Einkemmer Streamline integration as a method for two-dimensional elliptic grid generation Journal of Computational Physics 340, 435-450 (2017)

Psi is the radial coordinate and you can choose various discretizations of the first line

    std::unique_ptr<dg::geo::aGenerator2d> generator;
    //create the magnetic field
    dg::geo::TokamakMagneticField mag = dg::geo::createMagneticField(
            js["magnetic_field"]["params"]);
    //create a grid generator
    std::string type = js["grid"]["generator"]["type"].asString();
    int mode = 0;
    if( type != "dsp")
        mode = js["grid"]["generator"]["mode"].asInt();
    std::cout << "Constructing "<<type<<" grid ... \n";
    if( type == "flux")
        generator = std::make_unique<dg::geo::FluxGenerator>( mag.get_psip(),
                mag.get_ipol(), psi_0, psi_1, mag.R0(), 0., mode, false);
    else if( type == "orthogonal")
    {
        double psi_init = js["grid"]["generator"]["firstline"].asDouble();
        if( mode == 0 || mode == 1)
            generator = std::make_unique<dg::geo::SimpleOrthogonal>(
                mag.get_psip(), psi_0, psi_1, mag.R0(), 0., psi_init, mode);
        if( mode > 1)
        {
            dg::geo::CylindricalSymmTensorLvl1 lc =
                dg::geo::make_LiseikinCollective( mag.get_psip(), 0.1, 0.001);
            generator = std::make_unique<dg::geo::SimpleOrthogonal>(
                mag.get_psip(), lc, psi_0, psi_1, mag.R0(), 0., psi_init,
                mode%2);
        }
    }
    else if( type == "separatrix-orthogonal")
    {
        double RX = mag.R0()-1.1*mag.params().triangularity()*mag.params().a();
        double ZX = -1.1*mag.params().elongation()*mag.params().a();
        dg::geo::findXpoint( mag.get_psip(), RX, ZX);
        //dg::geo::CylindricalSymmTensorLvl1 monitor_chi;
        dg::geo::CylindricalSymmTensorLvl1 monitor_chi = dg::geo::make_Xconst_monitor( mag.get_psip(), RX, ZX) ;
        double fx = js["grid"]["generator"]["fx"].asDouble();
        generator = std::make_unique<dg::geo::SeparatrixOrthogonalAdaptor>(
            mag.get_psip(), monitor_chi, psi_0, RX, ZX, mag.R0(), 0., mode, false, fx);
        //psi_1 = -fx/(1.-fx)*psi_0;
    }
    else if ( type == "dsp")
    {
        double boxscaleRm  = js["grid"][ "scaleR"].get( 0u, 1.05).asDouble();
        double boxscaleRp  = js["grid"][ "scaleR"].get( 1u, 1.05).asDouble();
        double boxscaleZm  = js["grid"][ "scaleZ"].get( 0u, 1.05).asDouble();
        double boxscaleZp  = js["grid"][ "scaleZ"].get( 1u, 1.05).asDouble();
        const double Rmin=mag.R0()-boxscaleRm*mag.params().a();
        const double Zmin=-boxscaleZm*mag.params().a();
        const double Rmax=mag.R0()+boxscaleRp*mag.params().a();
        const double Zmax=boxscaleZp*mag.params().a();
        generator = std::make_unique<dg::geo::DSPGenerator>( mag,
            Rmin, Rmax, Zmin, Zmax, 2.*M_PI/(double)Nz);
    }
    else if( type == "ribeiro-flux")
        generator = std::make_unique<dg::geo::RibeiroFluxGenerator>( mag.get_psip(),
                psi_0, psi_1, mag.R0(), 0., mode, false);
    else if( type == "ribeiro")
        generator = std::make_unique<dg::geo::Ribeiro>( mag.get_psip(),
                psi_0, psi_1, mag.R0(), 0., mode, false);

Constructor & Destructor Documentation

SimpleOrthogonal() [1/2]

dg::geo::SimpleOrthogonal::SimpleOrthogonal ( const CylindricalFunctorsLvl2 &  psi, double  psi_0, double  psi_1, double  x0, double  y0, double  psi_firstline, int  mode = 0  )

inline

Construct a simple orthogonal grid.

Parameters

psi	\(\psi(x,y)\) is the flux function and its derivatives in Cartesian coordinates (x,y)
psi_0	first boundary (can be open)
psi_1	second boundary (can be open)
x0	a point on or close to the contour line given by psi_firstline
y0	a point on or close to the contour line given by psi_firstline
psi_firstline	psi value for first line discretization (must be a closed flux surface)
mode	Indicate mode used to create the first line discretization: 0 is conformal, 1 is an equalarc adaption

SimpleOrthogonal() [2/2]

dg::geo::SimpleOrthogonal::SimpleOrthogonal ( const CylindricalFunctorsLvl2 &  psi, const CylindricalSymmTensorLvl1 &  chi, double  psi_0, double  psi_1, double  x0, double  y0, double  psi_firstline, int  mode = 0  )

inline

Construct a simple orthogonal grid.

Parameters

psi	\(\psi(x,y)\) is the flux function and its derivatives in Cartesian coordinates (x,y)
chi	is the monitor tensor and its divergenc in Cartesian coordinates (x,y)
psi_0	first boundary (can be open)
psi_1	second boundary (can be open)
x0	a point on or close to the contour line given by psi_firstline
y0	a point on or close to the contour line given by psi_firstline
psi_firstline	psi value for first line discretization (must be a closed flux surface)
mode	Indicate mode used to create the first line discretization: 0 is conformal, 1 is an equalarc adaption

Member Function Documentation

clone()

virtual SimpleOrthogonal * dg::geo::SimpleOrthogonal::clone ( ) const

inlinefinaloverridevirtual

Abstract clone method that returns a copy on the heap.

Returns

a copy of *this on the heap

Implements dg::geo::aRealGenerator2d< real_type >.

f0()

double dg::geo::SimpleOrthogonal::f0 ( ) const

inline

The grid constant.

Returns

f_0 is the grid constant s.a. width() )

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The documentation for this struct was generated from the following file:

• simple_orthogonal.h