Fluidum

To install the package and its dependencies one can use julia import Pkg Pkg.add(url = "https://github.com/fafafrens/Fluidum.jl") After this one can use the package simply by using julia using Fluidum

Example 1+1 dimension

A simple example of running heavy quark simulations (actually is not simple at all since it is not understandable: what Observable does? what runFluidum ? Why we need 2 equations of state ? )

```julia using Fluidum

define equation of state and transport coefficients

eos = Heavy_Quark() viscosity=QGPViscosity(0.2,0.2) bulk=SimpleBulkViscosity(0.1,15.0) diffusion=ZeroDiffusion()

collect eos and transport coefficient in the FluidProperties struct

params=Fluidum.FluidProperties(eos,viscosity,bulk,diffusion)

define a radial grid

gridpoints=100 rmax=30 disc=CartesianDiscretization(OriginInterval(gridpoints,rmax))

define the name and number of fields, with appropriate parity

onedvischydro = onedvischydro=Fields( NDField((:even,),(:ghost,),:temperature), NDField((:odd,),(:ghost,),:ur), NDField((:even,),(:ghost,),:piphiphi), NDField((:even,),(:ghost,),:pietaeta), NDField((:even,),(:ghost,),:piB) )

discfields = DiscreteFileds(onedvisc_hydro,disc,Float64)

define a example function for the temperature

function temperature(r) 0.4*1/(exp(r/7)+1 )+0.0001 end

set the temperature field

phi=setarray((x)->temperature(x),:temperature,discfields);

define a time range for the evolution

tspan = (0.2,1000)

evolve until freeze-out temperature Tfo

freezeoutroutine(discfields,Fluidum.matrxi1dvisc!,params,phi,tspan;Tfo=0.1565) ```

Example 2+1 dimension

Instead you can also solve in 2 dimension ```julia using Fluidum

set up the fluid poroperties

fluidpropery=FluidProperties(FluiduMEoS(),SimpleShearViscosity(0.1,.1),ZeroBulkViscosity(),ZeroDiffusion())

the convention here are T, ux, uy, piyy, pizz, pixy, piB this has to match with the matrix defined

twodvischydro=Fields( NDField((:ghost,:ghost),(:ghost,:ghost),:temperature), NDField((:ghost,:ghost),(:ghost,:ghost),:ux), NDField((:ghost,:ghost),(:ghost,:ghost),:uy), NDField((:ghost,:ghost),(:ghost,:ghost),:piyy), NDField((:ghost,:ghost),(:ghost,:ghost),:pizz), NDField((:ghost,:ghost),(:ghost,:ghost),:pixy), NDField((:ghost,:ghost),(:ghost,:ghost),:piB) )

we define a 2 cartesian grid form -25 to 25 50 point each dimension

discretization=CartesianDiscretization(Fluidum.SymmetricInterval(50,25.),Fluidum.SymmetricInterval(50,25.))

we prepare the field with the discretization

twodvischydrodiscrete=DiscreteFileds(twodvisc_hydro,discretization,Float64)

#we define some random intial condition function temperature(r) 0.4(1+0.3rand())/(exp(abs(r)-10)+1 )+0.01 end

we set the array corresponding to the temperature

phi=setarray((x,y)->temperature(hypot(x,y)),:temperature,twodvischydrodiscrete);

using Plots

here to undertand whath we are doing

plot(phi[1,:,25])

this is the time span

tspan=(0.4,20)

this create the ODEProblem and feed it diffenential equations

res=oneshoot(twodvischydrodiscrete,Fluidum.matrxi2dvisc!,fluidpropery,phi,tspan)

plot the solution

using Plots plot(phi[1,:,25]) plot!(res[end][1,:,25]) ```

Citing

When using Fluidum.jl for research, teaching or similar, please cite our work, see CITATIONS.bib.