Advanced Usage

For more advanced examples please see the examples folder.

Accessing the ParticleField

FLOWVPM provides getter and setter functions for particles. Getter functions take the form get_property(P) where P is a particle, or get_property(pfield::ParticleField, i::Int) where i is the particle index. Getter functions return views. Setter functions take the from set_property(P, val) and set_property(pfield, i, val) where val is the new value to be set and is applied via broadcasting. Getter and setter functions are used by replacing "property" with the desired particle property such as get_X(P). The following are the particle properties:

X: position
Gamma: vortex strength
sigma: radius
vol: volume
circulation: circulation
U: velocity
vorticity: vorticity
J: velocity gradient
M: auxiliary computational storage
C: SFS model parameters
static: tag indicating whether this particle's states should evolve in time or not (sometimes used to represent solid bodies)
PSE: Storage needed for ParticleStrengthExchange
SFS: Storage of SFS values

Particle Field Settings

Here we provide details on all relevant keyword setting for a ParticleField. Settings (such as governing equations, fast multipole backend settings, and the turbulence model) are reviewed in the following subsections.

`formulation::Formulation`

The VPM formulation to be used. Options include:

rVPM: The reformulated VPM equations (default).
cVPM: The classic VPM equations.
formulation_tube_continuity: VPM equations derived from tube conservation of mass.
formulation_tube_momentum: VPM equations derived from tube conservation of momentum.

`viscous::ViscousScheme`

The viscous model used when propagating particles.

Inviscid: Uses no viscous modeling for the particles (default).
CoreSpreading: Uses a core spreading viscous model in which particles grow in size at each step. After a defined amount of time the particle size is reset and the particle strength recalculated to maintain the vorticity field strength.
ParticleStrengthExchange: Uses particle strength exchange to simulate viscosity.

`kernel::Kernel`

Regularization scheme used to de-singularize the vorticity and velocity fields.

singular: Singular vortex kernel (e.g. no regularization).
gaussian: Gaussian vortex kernel.
gaussianerf: Gaussian error function vortex kernel (default).
winckelmans: Winckelman vortex kernel

`UJ`

Function used to solve the $N$-body problem to obtain the velocity field, vorticity field, and subfilter scale contributions.

UJ_fmm: Uses the fast multipole method to solve the $N$-body problem (default).
UJ_direct: Loops through all particle interactions directly.

`Uinf::Function`

The freestream fluid velocity. Defaults to (t) -> SVector{3,Float64}(0,0,0).

`SFS::SubFilterScale`

The subfilter-scale (SFS) model used in the reformulated VPM equations. The SFS model simulated the turbulent energy cascade. For simulations with little turbulence the model may be unnecessary. Custom modifications can be made, setting the coefficient or the alpha used is possible.

noSFS: No SFS model is used (default).
SFS_Cs_nobackscatter: Uses a constant coefficient for the SFS model.
SFS_Cd_twolevel_nobackscatter: Uses a dynamic coefficient for the SFS model. Sets alpha=0.999. Recommended for high fidelity modeling.
SFS_Cd_threelevel_nobackscatter: Uses a dynamic coefficient for the SFS model. Sets alpha=0.667, which reduces the effect of the SFS significantly.

`integration`

The time integration scheme used in propogating particles states forward in time.

euler: Uses an euler time stepping scheme.
rungekutta3: Uses a low storage RK3 time stepping scheme (default).

`transposed::Bool`

Determines how the stretching term is calculated. Defaults to true, which is recommended for stability.

`relaxation::Relaxation`

Scheme used to ensure the field is divergence free.

norelaxation: Does nothing (e.g. no relaxation).
pedrizzetti: Relaxation scheme where the vortex strength is aligned with the local vorticity. (default).
correctedpedrizzetti: Relaxation scheme where the vortex strength is aligned with the local vorticity while preserving the magnitude of the particle strength.