olb::fd Namespace Reference

Namespaces
namespace	fdParams
namespace	tag

Classes
struct	AdNeumannZeroBoundaryScheme
struct	AdNeumannZeroBoundaryScheme< D, T, tag::CENTRAL >
struct	AdNeumannZeroBoundaryScheme< D, T, tag::UPWIND >
struct	AdvectionScheme
struct	AdvectionScheme< D, T, tag::CENTRAL >
struct	AdvectionScheme< D, T, tag::UPWIND >
struct	AdvectionScheme< D, T, tag::UPWIND_2_ORDER >
struct	DiffusionScheme
struct	DiffusionScheme< D, T, tag::CENTRAL >
struct	DiffusionScheme< D, T, tag::CENTRAL_WITH_ANTIDIFFUSIVITY >
struct	DirectedGradients2D
struct	DirectedGradients2D< T, DESCRIPTOR, direction, orientation, false >
struct	DirectedGradients2D< T, DESCRIPTOR, direction, orientation, true >
struct	DirectedGradients3D
struct	DirectedGradients3D< T, DESCRIPTOR, direction, orientation, deriveDirection, false >
struct	DirectedGradients3D< T, DESCRIPTOR, direction, orientation, deriveDirection, true >
struct	FdScheme

Functions
template<typename T , typename FIELD , typename CELL >
T *	accessOld (CELL cell, std::size_t iT) any_platform
template<typename T , typename FIELD , typename CELL >
T *	accessNew (CELL cell, std::size_t iT) any_platform
template<unsigned EXTENT>
constexpr unsigned	getArrayPos (const unsigned iExt, const unsigned iD) any_platform
template<typename T >
constexpr T	centralGradient (T u_p1, T u_m1) any_platform
	Second-order central gradient (u_p1 = u(x+1))
template<typename T >
constexpr T	boundaryGradient (T u_0, T u_1, T u_2) any_platform
	Second-order asymmetric gradient (u_1 = u(x+1))
template<typename T >
constexpr T	FSGradient (T u_0, T u_1, T u_2)
	Forward second-order first derivative.
template<typename T >
constexpr T	BSGradient (T u_0, T u_1, T u_2)
	Backward second-order first derivative.
template<typename T >
constexpr T	boundaryZeroGradient (T u_1, T u_2)
	Value at u_0 for which asymmetric gradient is zero (u_1 = u(x+1))
template<typename T >
constexpr T	centralSecondDeriv (T u_m1, T u_0, T u_p1) any_platform
	Second order central second derivative (u_p1 = u(x+1))
template<typename T >
constexpr T	centralSecondDeriv (T u_m2, T u_m1, T u_0, T u_p1, T u_p2) any_platform
	Forth order central second derivative (u_p1 = u(x+1))
template<typename T >
constexpr T	linearInterpolate (T u_0, T u_1, T pos)
	Linear interpolation (yields u0 at pos=0 and u1 at pos=1)
template<typename T >
constexpr T	d2u_dxdy (T u_xm1_ym1, T u_xm1_yp1, T u_xp1_ym1, T u_xp1_yp1) any_platform
	Second order mixed derivative (u_xp1_ym1 = u(x+1,y-1))
template<typename T >
constexpr T	d2u_dxdy (T u_xm1_ym1, T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1, T u_xp1_yp1) any_platform
	Second order mixed derivative (u_xp1_ym1 = u(x+1,y-1))
template<typename T >
constexpr T	laplacian2D (T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1) any_platform
	Second order Laplacian (u_xp1 = u(x+1,y))
template<typename T >
constexpr T	laplacian2D (T u_xm2, T u_ym2, T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1, T u_xp2, T u_yp2) any_platform
	Forth order Laplacian (u_xp1 = u(x+1,y))
template<typename T >
constexpr T	laplacian3D (T u_xm1, T u_ym1, T u_zm1, T u_0, T u_xp1, T u_yp1, T u_zp1) any_platform
	Second order Laplacian (symmetric, u_xp1 = u(x+1,y,z))
template<typename T >
constexpr T	laplacian3D (T u_xm2, T u_ym2, T u_zm2, T u_xm1, T u_ym1, T u_zm1, T u_0, T u_xp1, T u_yp1, T u_zp1, T u_xp2, T u_yp2, T u_zp2) any_platform
	Forth order Laplacian (symmetric, u_xp1 = u(x+1,y,z))

Function Documentation

accessNew()

template<typename T , typename FIELD , typename CELL >

T * olb::fd::accessNew	(	CELL	cell,
		std::size_t	iT )

Definition at line 56 of file fdAccessFunctions.h.

{
  return &cell.template getFieldPointer<FIELD>()[(iT+1) % 2];
}

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accessOld()

template<typename T , typename FIELD , typename CELL >

T * olb::fd::accessOld	(	CELL	cell,
		std::size_t	iT )

Definition at line 50 of file fdAccessFunctions.h.

{
  return &cell.template getFieldPointer<FIELD>()[iT % 2];
}

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boundaryGradient()

template<typename T >

T olb::fd::boundaryGradient ( T u_0, T u_1, T u_2 )

constexpr

Second-order asymmetric gradient (u_1 = u(x+1))

Definition at line 42 of file finiteDifference.h.

{
  return (-T{3}*u_0 + T{4}*u_1 - T{1}*u_2) / T{2};
}

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boundaryZeroGradient()

template<typename T >

T olb::fd::boundaryZeroGradient ( T u_1, T u_2 )

constexpr

Value at u_0 for which asymmetric gradient is zero (u_1 = u(x+1))

Definition at line 63 of file finiteDifference.h.

{
  return T{4}/T{3}*u_1 - T{1}/T{3}*u_2;
}

BSGradient()

template<typename T >

T olb::fd::BSGradient ( T u_0, T u_1, T u_2 )

constexpr

Backward second-order first derivative.

Definition at line 56 of file finiteDifference.h.

{
  return T{-1} * boundaryGradient(u_0, u_1, u_2);
}

References boundaryGradient().

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centralGradient()

template<typename T >

T olb::fd::centralGradient ( T u_p1, T u_m1 )

constexpr

Second-order central gradient (u_p1 = u(x+1))

Definition at line 35 of file finiteDifference.h.

{
  return (u_p1 - u_m1) / T{2};
}

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centralSecondDeriv() [1/2]

template<typename T >

T olb::fd::centralSecondDeriv ( T u_m1, T u_0, T u_p1 )

constexpr

Second order central second derivative (u_p1 = u(x+1))

Definition at line 74 of file finiteDifference.h.

{
  return u_m1 - T{2}*u_0 + u_p1;
}

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centralSecondDeriv() [2/2]

template<typename T >

T olb::fd::centralSecondDeriv ( T u_m2, T u_m1, T u_0, T u_p1, T u_p2 )

constexpr

Forth order central second derivative (u_p1 = u(x+1))

Definition at line 81 of file finiteDifference.h.

{
  return (- u_m2 + T{16}*u_m1 - T{30}*u_0 + T{16}*u_p1 - u_p2) / T{12};
}

d2u_dxdy() [1/2]

template<typename T >

T olb::fd::d2u_dxdy ( T u_xm1_ym1, T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1, T u_xp1_yp1 )

constexpr

Second order mixed derivative (u_xp1_ym1 = u(x+1,y-1))

Definition at line 45 of file finiteDifference2D.h.

{
  return - (u_xp1 + u_yp1 + u_xm1 + u_ym1 - T{2}*u_0 - u_xp1_yp1 - u_xm1_ym1) / T{2};
}

d2u_dxdy() [2/2]

template<typename T >

T olb::fd::d2u_dxdy ( T u_xm1_ym1, T u_xm1_yp1, T u_xp1_ym1, T u_xp1_yp1 )

constexpr

Second order mixed derivative (u_xp1_ym1 = u(x+1,y-1))

Definition at line 38 of file finiteDifference2D.h.

{
  return (u_xp1_yp1 - u_xp1_ym1 - u_xm1_yp1 + u_xm1_ym1) / T{4};
}

FSGradient()

template<typename T >

T olb::fd::FSGradient ( T u_0, T u_1, T u_2 )

constexpr

Forward second-order first derivative.

Definition at line 49 of file finiteDifference.h.

{
  return boundaryGradient(u_0, u_1, u_2);
}

References boundaryGradient().

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getArrayPos()

template<unsigned EXTENT>

unsigned olb::fd::getArrayPos ( const unsigned iExt, const unsigned iD )

constexpr

Definition at line 63 of file fdAccessFunctions.h.

{
  return iExt*EXTENT + iD;
}

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laplacian2D() [1/2]

template<typename T >

T olb::fd::laplacian2D ( T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1 )

constexpr

Second order Laplacian (u_xp1 = u(x+1,y))

Definition at line 53 of file finiteDifference2D.h.

{
  return u_xm1 + u_ym1 + u_xp1 + u_yp1 - T{4}*u_0;
}

laplacian2D() [2/2]

template<typename T >

T olb::fd::laplacian2D ( T u_xm2, T u_ym2, T u_xm1, T u_ym1, T u_0, T u_xp1, T u_yp1, T u_xp2, T u_yp2 )

constexpr

Forth order Laplacian (u_xp1 = u(x+1,y))

Definition at line 60 of file finiteDifference2D.h.

{
  return (-T{60}*u_0 + T{16}*(u_xm1 + u_ym1 + u_xp1 + u_yp1)
         - (u_xm2 + u_ym2 + u_xp2 + u_yp2)) / T{12};
}

laplacian3D() [1/2]

template<typename T >

T olb::fd::laplacian3D ( T u_xm1, T u_ym1, T u_zm1, T u_0, T u_xp1, T u_yp1, T u_zp1 )

constexpr

Second order Laplacian (symmetric, u_xp1 = u(x+1,y,z))

Definition at line 39 of file finiteDifference3D.h.

{
  return u_xm1 + u_ym1 + u_zm1 + u_xp1 + u_yp1 + u_zp1 - T{6}*u_0;
}

laplacian3D() [2/2]

template<typename T >

T olb::fd::laplacian3D ( T u_xm2, T u_ym2, T u_zm2, T u_xm1, T u_ym1, T u_zm1, T u_0, T u_xp1, T u_yp1, T u_zp1, T u_xp2, T u_yp2, T u_zp2 )

constexpr

Forth order Laplacian (symmetric, u_xp1 = u(x+1,y,z))

Definition at line 46 of file finiteDifference3D.h.

{
  return (-T{90}*u_0 + T{16}*(u_xm1 + u_ym1 + u_zm1 + u_xp1 + u_yp1 + u_zp1)
         - (u_xm2 + u_ym2 + u_zm2 + u_xp2 + u_yp2 + u_zp2)) / T{12};
}

linearInterpolate()

template<typename T >

T olb::fd::linearInterpolate ( T u_0, T u_1, T pos )

constexpr

Linear interpolation (yields u0 at pos=0 and u1 at pos=1)

Definition at line 92 of file finiteDifference.h.

{
  return (T{1}-pos)*u_0 + pos*u_1;
}