SPH Kernels¶
Definition of some SPH kernel functions
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class
pysph.base.kernels.
CubicSpline
(dim=1)[source]¶ Bases:
object
Cubic Spline Kernel: [Monaghan1992]
W(q)= σ3[1−32q2(1−q2)], for 0≤q≤1,= σ34(2−q)3,for 1<q≤2,= 0,for q>2,where σ3 is a dimensional normalizing factor for the cubic spline function given by:
σ3= 23h1,for dim=1,σ3= 107πh2, for dim=2,σ3= 1πh3,for dim=3.References
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class
pysph.base.kernels.
Gaussian
(dim=2)[source]¶ Bases:
object
Gaussian Kernel: [Liu2010]
W(q)= σge−q2, for 0≤q≤3,= 0,for q>3,where σg is a dimensional normalizing factor for the gaussian function given by:
σg= 1π1/2h1, for dim=1,σg= 1πh2, for dim=2,σg= 1π3/2h3,for dim=3.References
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class
pysph.base.kernels.
QuinticSpline
(dim=2)[source]¶ Bases:
object
Quintic Spline SPH kernel: [Liu2010]
W(q)= σ5[(3−q)5−6(2−q)5+15(1−q)5], for 0≤q≤1,= σ5[(3−q)5−6(2−q)5],for 1<q≤2,= σ5 (3−q)5,for 2<q≤3,= 0,for q>3,where σ5 is a dimensional normalizing factor for the quintic spline function given by:
σ5= 120h1,for dim=1,σ5= 7478πh2, for dim=2,σ5= 3359πh3,for dim=3.Raises: NotImplementedError
– Quintic spline currently only supports 2D kernels.