Kernel.h File Reference

SPH kernels. More...

#include "objects/containers/Array.h"
#include "objects/geometry/Vector.h"

Go to the source code of this file.

Classes
class	Kernel< TDerived, D >
	Base class for all SPH kernels. More...
class	LutKernel< D >
	A look-up table approximation of the kernel. More...
class	CubicSpline< D >
	Cubic spline (M4) kernel. More...
class	FourthOrderSpline< D >
	Fourth-order spline (M5) kernel. More...
class	CoreTriangle
	Kernel proposed by Read et al. (2010) with improved stability. More...
class	ThomasCouchmanKernel< D >
	Kernel introduced by Thomas & Couchman (1992). More...
class	WendlandC2
class	WendlandC4
class	WendlandC6
class	Gaussian< D >
	Gaussian kernel. More...
class	TriangleKernel< D >
	Triangular (piecewise linear) kernel. More...
class	ScalingKernel< D, TKernel >
	Helper kernel wrapper that modifies the support of another kernel. More...
class	SymmetrizeValues< TKernel >
class	SymmetrizeSmoothingLengths< TKernel >
struct	IsKernel< T, typename >
struct	IsKernel< T, VoidType< decltype(std::declval< T >().radius())> >

Functions
template<typename T >
INLINE T	laplacian (const T &value, const Vector &grad, const Vector &dr)
	SPH approximation of laplacian, computed from a kernel gradient. More...
INLINE Vector	gradientOfDivergence (const Vector &value, const Vector &grad, const Vector &dr)
	Second derivative of vector quantity, applying gradient on a divergence. More...

Detailed Description

SPH kernels.

Author

Pavel Sevecek (sevecek at sirrah.troja.mff.cuni.cz))

Date

2016-2021

Definition in file Kernel.h.

Function Documentation

gradientOfDivergence()

INLINE Vector gradientOfDivergence	(	const Vector &	value,
		const Vector &	grad,
		const Vector &	dr
	)

Second derivative of vector quantity, applying gradient on a divergence.

Doesn't make sense for scalar quantities. See Price 2010 [Price_2010]

Definition at line 527 of file Kernel.h.

laplacian()

template<typename T >

INLINE T laplacian	(	const T &	value,
		const Vector &	grad,
		const Vector &	dr
	)

SPH approximation of laplacian, computed from a kernel gradient.

Is more stable than directly applying second derivatives to kernel and has the same error O(h^2). Can be used to compute laplacian of both scalar and vector quantities.

Parameters

value	Scalar or vector value from which we compute the laplacian
grad	Kernel gradient corresponding to vector dr

Note

Note that the sign is different compared to the Eq. (95) of [Price_2010]. This is correct, provided the value is computed as v[j]-v[i], dr is computed as r[j]-r[i] and grad is computed as grad W(r[j]-r[i]).

Definition at line 519 of file Kernel.h.