Viscous Scheme

`ViscousScheme{R}`

Type declaring viscous scheme.

Implementations must have the following properties: * nu::R : Kinematic viscosity.

Inviscid()

Creates an inviscid scheme with zero kinematic viscosity.

CoreSpreading(nu, sgm0, zeta::Tzeta=zeta_fmm; <keyword arguments>)

Creates a core spreading viscous scheme with the given parameters.

Arguments

• nu::Real Kinematic viscosity.
• sgm0::Real Core size after reset.
• zeta::Function = zeta_fmm Basis function evaluation method.
• beta::Real = 1.5 Maximum core size growth σ/σ_0.
• itmax::Int = 15 Maximum number of RBF iterations.
• tol::Real = 1e-3 RBF interpolation tolerance.
• iterror::Bool = true Throw error if RBF didn't converge.
• verbose::Bool = false Verbose on RBF interpolation.
• v_lvl::Int = 2 Verbose printing tab level.
• debug::Bool = false Print verbose for debugging.
• rbf::Function = rbf_conjugategradient RBF function.
• rr0s::Array{R, 1} = zeros(R, 3) Initial field residuals.
• rrs::Array{R, 1} = zeros(R, 3) Current field residuals.
• prev_rrs::Array{R, 1} = zeros(R, 3) Previous field residuals.
• pAps::Array{R, 1} = zeros(R, 3) pAp product.
• alphas::Array{R, 1} = zeros(R, 3) Alpha coefficients.
• betas::Array{R, 1} = zeros(R, 3)
• flags::Array{Bool, 1} = zeros(Bool, 3)

ParticleStrengthExchange(nu; <keyword arguments>)

Creates a particle strength exchange viscous scheme with the given parameters.

Arguments

• nu::Real Kinematic viscosity.
• recalculate_vols::Bool = true Whether to recalculate particle volumes.

Radial basis function interpolation of Gamma using the conjugate gradient method. This method only works on a particle field with uniform smoothing radius sigma.

See 20180818 notebook and https://en.wikipedia.org/wiki/Conjugategradientmethod#Theresultingalgorithm