CppNoddy::Example Namespace Reference

Classes
class	Acoustic_1d
	Define the system. More...
class	Acoustic_1d_ref
	Define the system. More...
class	Arc_problem
	Define the residual for arc-length continuation of a circle. More...
class	BC_lower
class	BC_upper
class	Berman_equation
	Define the Berman equation by inheriting Equation base class. More...
class	Berman_left_BC
class	Berman_residual
	Define a residual function using the boundary conditions for the Berman equation. More...
class	Berman_right_BC
class	Biharmonic_equation
	Define the biharmonic eigenvalue equation by inheriting Equation base class. More...
class	Biharmonic_residual
	Define a residual function using the boundary conditions for the biharmonic_equation. More...
class	Blasius_equation
	Define the Blasius equation by inheriting Equation base class. More...
class	Blasius_left_BC
class	Blasius_residual
	Define a residual function using the boundary conditions for the Blasius profile. More...
class	Blasius_right_BC
class	Cube_root_problem
	The problem to be solved, here z^3 -1 in complex form. More...
class	dd_BC
class	Diff_both_BC
class	Diff_equation
class	diffusion_double
class	Diffusion_equations
class	Diffusion_left_BC
	Define the boundary conditions. More...
class	Diffusion_right_BC
class	Euler_1d
	Define the system. More...
class	FS_eqn
	Define the Falkner-Skan equation. More...
class	FS_residual
	Define a residual function using the boundary conditions for the Blasius profile. More...
class	harmonic_both_BC
class	harmonic_equation
	Define the harmonic equation by inheriting the Equation base class. More...
class	Harmonic_equation
	Define the harmonic equation by inheriting the Equation base class. More...
class	Harmonic_left_BC
class	Harmonic_right_BC
class	Karman_equations
	Define the Karman equations. More...
class	Karman_left_BC
	Define the boundary conditions. More...
class	Karman_right_BC
class	Lorenz_equations
	Define the Lorenz equations by inheriting Equation base class. More...
class	Neutral_residual
class	Nlin_adv_equation
class	Nlin_adv_left_BC
class	Nlin_adv_right_BC
class	NlinAdv
	Define the system. More...
class	Nonidentity_equation
	Define the harmonic equation by inheriting the Equation base class. More...
class	Nonidentity_left_BC
class	Nonidentity_right_BC
class	nonlinear
class	OS_bvp_equation
	Define the OSE for the local refinement procedure. More...
class	OS_bvp_left_BC
class	OS_bvp_right_BC
class	OS_evp_both_BC
class	OS_evp_equation
	Define the OS equation for the global QZ EVP. More...
class	Shallow_1d_rad
	Define the system. More...
class	Shallow_2d_rad
	Define the system. More...
class	Shallow_2d_source
	Define the system. More...
class	Troesch_equation
	Define the harmonic equation by inheriting the Equation base class. More...
class	Troesch_left_BC
class	Troesch_right_BC
class	VCube_root_problem
	Defines the problem: here z^3 -1 = 0, in vector form using real and imaginary parts. More...

Functions
double	source (const double &x, const double &y, const double &t)
const D_complex	eye (0., 1.0)
const double	delta (0.5)
D_complex	z (double x)
D_complex	zx (double x)
D_complex	zxx (double x)
double	U (double y)
	Globally define the base flow. More...
double	Udd (double y)
	Globally define the base flow curvature. More...
int	MAX_REFINE (3)
D_complex	U (const D_complex &y)
D_complex	Udd (const D_complex &y)
void	Qfn (const double &x, double &f)
	The function that defines the integrand. More...
void	test (unsigned n)
	The test will fail if it requires more than a set number of subintervals in the integration to converge to the exact value to within the specified tol. More...
D_complex	Cfn (const D_complex &z)
	A std::complex function for z^3 - 1. More...
double	K (4.0)
	bulk modulus More...
double	rho_big (4.0)
	higher density More...
double	rho_small (1.0)
	lower density More...
double	rho (const double &x)
	Density function for the medium. More...
void	Q_init (const double &x, DenseVector< double > &q)
	Set the initial state of the system. More...
double	K (2.0)
	bulk modulus More...
double	rho (2.0)
	higher density More...
double	g (1.0)
	gravitational acceleration More...
double	A (1.0)
	initial hump amplitude More...
double	gamma (1.4)
	Adiabatic index – ratio of specific heats. More...
void	Q_init (const double &x, const double &y, DenseVector< double > &q)
	Set the initial state of the system. More...
double	g (9.81)
	gravitational acceleration More...
double	A (0.2)
	hump amplitude More...
double	z (const double &x, const double &y)
	Topography shape. More...
double	A (10.0)
double	sigma (100.0)
double	W_inf (0.0)
double	W_disk (1.0)
const double	eps (2.0)
double	source (const double &y, const double &t)
double	source_fn (const std::pair< double, double > &coord)
double	boundary_fn (const std::pair< double, double > &coord)

Variables
double	s
	relative rotation rate More...
double	Re
	Globally define the Reynolds number and wavenumber. More...
double	alpha
double	wave_speed
	The phase speed of the instability. More...
OneD_Node_Mesh< D_complex, D_complex >	baseflow
bool	failed = false

Function Documentation

A() [1/3]

double CppNoddy::Example::A

(

0.

2

)

hump amplitude

A() [2/3]

double CppNoddy::Example::A

(

1.

0

)

initial hump amplitude

Referenced by CppNoddy::Example::Diffusion_equations::residual_fn(), and z().

A() [3/3]

double CppNoddy::Example::A

(

10.

0

)

boundary_fn()

double CppNoddy::Example::boundary_fn

(

const std::pair< double, double > &

coord

)

Definition at line 26 of file PoissonCartesian_petscd_mumps.cpp.

                                                              {
      double x = coord.first; double y = coord.second;
      return x*x*y*y;
    }

Cfn()

D_complex CppNoddy::Example::Cfn ( const D_complex &  z )

inline

A std::complex function for z^3 - 1.

Definition at line 13 of file TrivialComplex.cpp.

    {
      return z * z * z - 1.;
    }

References z().

delta()

const double CppNoddy::Example::delta

(

0.

5

)

Referenced by CppNoddy::Example::Shallow_2d_source::source_fn(), z(), zx(), and zxx().

eps()

const double CppNoddy::Example::eps

(

2.

0

)

Referenced by source().

eye()

const D_complex CppNoddy::Example::eye	(	0.	,
		1.	0
	)

Referenced by z(), zx(), and zxx().

g() [1/2]

double CppNoddy::Example::g

(

1.

0

)

gravitational acceleration

Referenced by CppNoddy::Example::Shallow_1d_rad::flux_fn(), CppNoddy::Example::Shallow_2d_rad::flux_fn_x(), CppNoddy::Example::Shallow_2d_source::flux_fn_x(), CppNoddy::Example::Shallow_2d_rad::flux_fn_y(), CppNoddy::Example::Shallow_2d_source::flux_fn_y(), CppNoddy::Example::Shallow_2d_rad::Jac_flux_fn_x(), CppNoddy::Example::Shallow_2d_source::Jac_flux_fn_x(), CppNoddy::Example::Shallow_2d_rad::Jac_flux_fn_y(), CppNoddy::Example::Shallow_2d_source::Jac_flux_fn_y(), CppNoddy::Example::Shallow_1d_rad::max_charac_speed(), CppNoddy::Example::Shallow_2d_rad::max_charac_speed(), CppNoddy::Example::Shallow_2d_source::max_charac_speed(), CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::Nonidentity_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::Troesch_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::OS_evp_equation::residual_fn(), CppNoddy::Example::OS_bvp_equation::residual_fn(), CppNoddy::Example::Berman_equation::residual_fn(), CppNoddy::Example::Blasius_equation::residual_fn(), CppNoddy::Example::harmonic_equation::residual_fn(), CppNoddy::Example::Diff_equation::residual_fn(), and CppNoddy::Example::Shallow_2d_source::source_fn().

g() [2/2]

double CppNoddy::Example::g

(

9.

81

)

gravitational acceleration

gamma()

double CppNoddy::Example::gamma

(

1.

4

)

Adiabatic index – ratio of specific heats.

Referenced by CppNoddy::Example::Euler_1d::flux_fn(), and CppNoddy::Example::Euler_1d::max_charac_speed().

K() [1/2]

double CppNoddy::Example::K

(

2.

0

)

bulk modulus

K() [2/2]

double CppNoddy::Example::K

(

4.

0

)

bulk modulus

Referenced by CppNoddy::Example::Acoustic_1d::flux_fn(), CppNoddy::Example::Acoustic_1d_ref::flux_fn(), CppNoddy::Example::Acoustic_1d::max_charac_speed(), CppNoddy::Example::Acoustic_1d_ref::max_charac_speed(), and Q_init().

MAX_REFINE()

int CppNoddy::Example::MAX_REFINE

(

3

)

Referenced by CppNoddy::Example::Neutral_residual::Neutral_residual().

Q_init() [1/2]

void CppNoddy::Example::Q_init	(	const double &	x,
		const double &	y,
		DenseVector< double > &	q
	)

Set the initial state of the system.

Definition at line 46 of file HYP2DLinearAdvectionXY.cpp.

    {
      if ( ( std::abs( x ) < 0.25 ) && ( std::abs( y ) < 0.25 ) )
      {
        q[ 0 ]  = 1.0;
      }
      else
      {
        q[ 0 ] = 0.0;
      }
    }

Q_init() [2/2]

void CppNoddy::Example::Q_init	(	const double &	x,
		DenseVector< double > &	q
	)

Set the initial state of the system.

Definition at line 71 of file HYPAcousticImpedance.cpp.

    {
      if ( ( x < -1.5 ) && ( x > -2.5 ) )
      {
        q[ p ] = 1.0;
        q[ u ] = q[ p ] / sqrt( K * rho( x ) );
      }
      else
      {
        q[ p ] = q[ u ] = 0.0;
      }
    }

References K(), p, rho, and u.

Qfn()

void CppNoddy::Example::Qfn	(	const double &	x,
		double &	f
	)

The function that defines the integrand.

Definition at line 19 of file Quadrature.cpp.

    {
      f = std::cos( x ) * std::exp( -x / 4. );
    }

References f.

rho() [1/2]

double CppNoddy::Example::rho

(

2.

0

)

higher density

rho() [2/2]

double CppNoddy::Example::rho

(

const double &

x

)

Density function for the medium.

Definition at line 30 of file HYPAcousticImpedance.cpp.

    {
      if ( std::abs( x ) < 1.0 )
      {
        return rho_small;
      }
      else
      {
        return rho_big;
      }
    }

References rho_big(), and rho_small().

rho_big()

double CppNoddy::Example::rho_big

(

4.

0

)

higher density

Referenced by rho().

rho_small()

double CppNoddy::Example::rho_small

(

1.

0

)

lower density

Referenced by CppNoddy::Example::Acoustic_1d::max_charac_speed(), and rho().

sigma()

double CppNoddy::Example::sigma

(

100.

0

)

Referenced by CppNoddy::Example::Diffusion_equations::matrix0(), and CppNoddy::Example::Diffusion_equations::residual_fn().

source() [1/2]

double CppNoddy::Example::source	(	const double &	x,
		const double &	y,
		const double &	t
	)

Definition at line 26 of file IBVPLinear.cpp.

    {
      return - 2 * std::exp( -x*t ) + ( 1 - y * y ) * ( x + t ) * std::exp( -x*t );
    }

Referenced by CppNoddy::Example::diffusion_double::residual_fn(), CppNoddy::Example::nonlinear::residual_fn(), and CppNoddy::Example::Nlin_adv_equation::residual_fn().

source() [2/2]

double CppNoddy::Example::source	(	const double &	y,
		const double &	t
	)

Definition at line 32 of file IBVPNonlinearAdvDiffusion.cpp.

    {
      return ( 1 + y + eps * y * ( 1 - y ) * std::exp( -t ) ) * eps * y * ( 1 - y ) * std::exp( -t )
             - 2 * eps * std::exp( - t ) / Re;
    }

References eps(), and Re.

source_fn()

double CppNoddy::Example::source_fn

(

const std::pair< double, double > &

coord

)

Definition at line 21 of file PoissonCartesian_petscd_mumps.cpp.

                                                            {
      double x = coord.first; double y = coord.second;
      return 2*(x*x + y*y);
    }

test()

void CppNoddy::Example::test

(

unsigned

n

)

The test will fail if it requires more than a set number of subintervals in the integration to converge to the exact value to within the specified tol.

Definition at line 27 of file Quadrature.cpp.

    {
      if ( n > 16777216 )
      {
        failed = true;
      }
    }

References failed.

U() [1/2]

D_complex CppNoddy::Example::U

(

const D_complex &

y

)

Definition at line 23 of file EVPRayleigh_lapack.cpp.

    {
      return std::sin( y );
    }

U() [2/2]

double CppNoddy::Example::U

(

double

y

)

Globally define the base flow.

Definition at line 36 of file EVPOrrSommerfeldEasy_lapack.cpp.

    {
      return 1.0 - y * y;
    };

Udd() [1/2]

D_complex CppNoddy::Example::Udd

(

const D_complex &

y

)

Definition at line 28 of file EVPRayleigh_lapack.cpp.

    {
      return - std::sin( y );
    }

Udd() [2/2]

double CppNoddy::Example::Udd

(

double

y

)

Globally define the base flow curvature.

Definition at line 41 of file EVPOrrSommerfeldEasy_lapack.cpp.

    {
      return -2.0;
    };

Referenced by CppNoddy::Example::OS_evp_equation::residual_fn(), and CppNoddy::Example::OS_bvp_equation::residual_fn().

W_disk()

double CppNoddy::Example::W_disk

(

1.

0

)

Referenced by CppNoddy::Example::Karman_left_BC::residual_fn().

W_inf()

double CppNoddy::Example::W_inf

(

0.

0

)

Referenced by CppNoddy::Example::Karman_left_BC::residual_fn(), CppNoddy::Example::Karman_right_BC::residual_fn(), and CppNoddy::Example::Karman_equations::residual_fn().

z() [1/2]

double CppNoddy::Example::z	(	const double &	x,
		const double &	y
	)

Topography shape.

Definition at line 22 of file HYP2DShallowSource.cpp.

    {
      // to compare with our 1D formulation, we'll make it independent
      // of the transverse y-coordinate
      double rsq( ( x - 10 ) * ( x - 10 ) + 0.0 * y * y );
      return A * std::exp( - 0.5 * rsq );
    }

References A().

z() [2/2]

D_complex CppNoddy::Example::z

(

double

x

)

Definition at line 29 of file EVPHarmonicComplex_lapack.cpp.

                            {
      return x + eye*delta*x*(1-x);
    }

References delta(), and eye().

Referenced by Cfn(), CppNoddy::Example::Harmonic_right_BC< _Type >::Harmonic_right_BC(), CppNoddy::Example::Karman_equations::jacobian(), CppNoddy::Example::Nonidentity_equation< _Type, _Xtype >::matrix0(), CppNoddy::Example::Diffusion_equations::matrix0(), CppNoddy::Example::Nlin_adv_equation::matrix1(), CppNoddy::Example::nonlinear::matrix2(), CppNoddy::Example::Nonidentity_right_BC< _Type >::Nonidentity_right_BC(), CppNoddy::Example::Harmonic_right_BC< _Type >::residual_fn(), CppNoddy::Example::Nonidentity_right_BC< _Type >::residual_fn(), CppNoddy::Example::Troesch_left_BC< _Type >::residual_fn(), CppNoddy::Example::Troesch_right_BC< _Type >::residual_fn(), CppNoddy::Example::Harmonic_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::Nonidentity_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::Troesch_equation< _Type, _Xtype >::residual_fn(), CppNoddy::Example::Harmonic_left_BC< _Type >::residual_fn(), CppNoddy::Example::OS_evp_both_BC::residual_fn(), CppNoddy::Example::OS_bvp_left_BC::residual_fn(), CppNoddy::Example::OS_bvp_right_BC::residual_fn(), CppNoddy::Example::Biharmonic_equation::residual_fn(), CppNoddy::Example::Cube_root_problem::residual_fn(), CppNoddy::Example::OS_evp_equation::residual_fn(), CppNoddy::Example::OS_bvp_equation::residual_fn(), CppNoddy::Example::Berman_left_BC::residual_fn(), CppNoddy::Example::Berman_right_BC::residual_fn(), CppNoddy::Example::Blasius_left_BC::residual_fn(), CppNoddy::Example::Blasius_right_BC::residual_fn(), CppNoddy::Example::Karman_left_BC::residual_fn(), CppNoddy::Example::Karman_right_BC::residual_fn(), CppNoddy::Example::dd_BC::residual_fn(), CppNoddy::Example::BC_lower::residual_fn(), CppNoddy::Example::BC_upper::residual_fn(), CppNoddy::Example::harmonic_both_BC::residual_fn(), CppNoddy::Example::Diff_both_BC::residual_fn(), CppNoddy::Example::Diffusion_left_BC::residual_fn(), CppNoddy::Example::Diffusion_right_BC::residual_fn(), CppNoddy::Example::Nlin_adv_left_BC::residual_fn(), CppNoddy::Example::Nlin_adv_right_BC::residual_fn(), CppNoddy::Example::Arc_problem::residual_fn(), CppNoddy::Example::FS_eqn::residual_fn(), CppNoddy::Example::FS_residual::residual_fn(), CppNoddy::Example::Berman_equation::residual_fn(), CppNoddy::Example::Blasius_equation::residual_fn(), CppNoddy::Example::Karman_equations::residual_fn(), CppNoddy::Example::diffusion_double::residual_fn(), CppNoddy::Example::nonlinear::residual_fn(), CppNoddy::Example::Neutral_residual::residual_fn(), CppNoddy::Example::VCube_root_problem::residual_fn(), CppNoddy::Example::Diffusion_equations::residual_fn(), CppNoddy::Example::Nlin_adv_equation::residual_fn(), CppNoddy::Example::Lorenz_equations::residual_fn(), CppNoddy::Example::harmonic_equation::residual_fn(), CppNoddy::Example::Diff_equation::residual_fn(), and CppNoddy::Example::Shallow_2d_source::source_fn().

zx()

D_complex CppNoddy::Example::zx

(

double

x

)

Definition at line 33 of file EVPHarmonicComplex_lapack.cpp.

                             {
      return 1.0 + eye*delta*(1-2.*x);
    }

References delta(), and eye().

zxx()

D_complex CppNoddy::Example::zxx

(

double

x

)

Definition at line 37 of file EVPHarmonicComplex_lapack.cpp.

                              {
      return -eye*2.*delta;
    }

References delta(), and eye().

Variable Documentation

alpha

double CppNoddy::Example::alpha

Definition at line 34 of file EVPOrrSommerfeldEasy_lapack.cpp.

Referenced by CppNoddy::Example::OS_evp_equation::matrix1(), CppNoddy::Example::OS_evp_equation::residual_fn(), and CppNoddy::Example::OS_bvp_equation::residual_fn().

baseflow

OneD_Node_Mesh<D_complex, D_complex> CppNoddy::Example::baseflow

Definition at line 19 of file EVPRayleigh_lapack.cpp.

failed

bool CppNoddy::Example::failed = false

Definition at line 16 of file Quadrature.cpp.

Referenced by test().

Re

double CppNoddy::Example::Re

Globally define the Reynolds number and wavenumber.

Definition at line 34 of file EVPOrrSommerfeldEasy_lapack.cpp.

Referenced by CppNoddy::Example::Berman_residual::Berman_residual(), CppNoddy::Example::Nlin_adv_equation::get_jacobian_of_matrix1_mult_vector(), CppNoddy::Example::OS_evp_equation::matrix1(), CppNoddy::Example::Nlin_adv_equation::matrix1(), CppNoddy::Example::OS_evp_equation::residual_fn(), CppNoddy::Example::OS_bvp_equation::residual_fn(), CppNoddy::Example::Neutral_residual::residual_fn(), and source().

s

double CppNoddy::Example::s

relative rotation rate

Definition at line 30 of file BVPKarmanArclength.cpp.

Referenced by CppNoddy::Example::Karman_right_BC::residual_fn(), and CppNoddy::Example::Karman_equations::residual_fn().

wave_speed

double CppNoddy::Example::wave_speed

The phase speed of the instability.

Definition at line 34 of file EVPOrrSommerfeldNeutralCurve_lapack.cpp.

Referenced by CppNoddy::Example::Neutral_residual::residual_fn().