add viscosity kernel

src/kernels.jl

@@ -66,3 +66,32 @@ end
 
 @inline W(k::KernelPoly6,r2) =  k.coeff * (k.h² - r2)^3
 @inline ∇W(k::KernelPoly6,rij,r = norm(rij)) = k.coeff_grad * (k.h² - r^2)^2 * rij
+
+
+
+function KernelViscosity(N,h::T) where T
+    coeff = (N-1)*N*(N+2)*(N+3) / (6*h^N * surface_hypersphere(N))
+    coeff_grad = 1.0
+    KernelViscosity{N,T}(h,coeff,coeff_grad)
+end
+
+@inline function W(k::KernelViscosity,r2)
+    r = sqrt(r2)
+    rh = r/k.h
+
+    return k.coeff * (-0.5 * rh^3 + rh^2 + 0.5/rh - 1)
+end
+
+@inline function ∇W(k::KernelViscosity,rij,r = norm(rij))
+    rh = r/k.h
+
+    return k.coeff * (-1.5 * rh^2 + 2*rh - 0.5/(rh^2)) / k.h * rij/r
+end
+
+
+@inline function ∇²W(k::KernelViscosity,r2)
+    r = sqrt(r2)
+    rh = r/k.h
+    #TODO
+    return 0
+end

src/types.jl

@@ -15,6 +15,13 @@ struct KernelPoly6{N,T} <: Kernel{N} where T <: Number
     coeff_grad::T
 end
 
+
+struct KernelViscosity{N,T} <: Kernel{N} where T <: Number
+    h::T
+    coeff::T
+    coeff_grad::T
+end
+
 struct Particle{N,T}
     x::SVector{N,T} # position
     v::SVector{N,T} # velocity

test/runtests.jl

@@ -1,11 +1,11 @@
 using Test
 using LinearAlgebra
-import SmoothedParticleHydrodynamics: forces!, update!, surface_hypersphere, KernelSpiky,KernelPoly6, Kernel, W, ∇W, Particle
+import SmoothedParticleHydrodynamics: forces!, update!, surface_hypersphere, KernelSpiky,KernelPoly6, Kernel, W, ∇W, Particle, KernelViscosity
 
 
 function numerical_integration(k::Kernel{N},dr) where N
     integral = 0.
-        for r = 0:dr:k.h
+        for r = dr/2:dr:k.h
             r2 = r^2
             integral = integral + W(k,r2)*surface_hypersphere(N)*r^(N-1)*dr
         end
@@ -31,7 +31,7 @@ end
 
     rij = [2.,3.,4.]
 
-    for kernel in (KernelSpiky,KernelPoly6)
+    for kernel in (KernelSpiky,KernelPoly6,KernelViscosity)
         for N = 2:4
             local k
             k = kernel(N,h)