VMSAdjoint

How to use the package:

Tutorial

In this tutorial we are going to see how to obtain the sensitivities on a NACA 0012 airfoil using the Variational MultiScale Adjoint.

Start loading the packages julia using AirfoilTools using VMSAdjoint using Gridap, GridapGmsh using SegregatedVMSSolver.ParametersDef

Define the physical parameters of the simulation julia fname = "n0012.csv" #file name with the coordinates to load AoA = 2.5 #angle of attack, in degrees Re = 1000 #Reynolds number uin = [1.0,0.0] #inlet velocity order = 2 #order of the elements

Define the parametrization of the airfoil. In this case we are using control points on the top and bottom surface of the airfoil. We define the x-coordinates of them, the y-coordinates are computed when we create the Design.

```julia ap0 = getairfoilcoordinates(joinpath(@DIR, fname))

40 control points in total, 20 on the suction side, 20 on the pressure side

controlpx = collect(LinRange(0.05,0.95,20)) controlpoints = ControlPoints(controlpx,controlpx)

R = 0.15 #support radius RBFfun = RBFFunctionLocalSupport(RBFCP4, R) #RBFCP4 is the Radial Basis Function

rbfg = RBFGeometry(control_points,RBFfun) rbfd = RBFDesign(rbfg, ap0) ```

We econde the values of the simulation. ```julia

sprob = StabilizedProblem(VMS(order))

physicalp = PhysicalParameters(Re=Re, uin=uin) timep = TimeParameters(dt=0.05, tF=1.0, timewindow=(0.8, 1.0)) #the time-window define the time-span for time-averaging

meshinfo = AirfoilMesh(AoA= AoA, meshref=1) #increasing meshref, we increse the resolution of the mesh in the domain meshp = MeshParameters((1,1), 2, meshinfo) exportp = ExportParameters(printinitial=true,printmodel=true,name_tags=["airfoil"], fieldexport=[["uh","ph","friction"]])

solverp = SolverParameters(θ=1.0, M=1, matrixfrequpdate=4)

simparams = SimulationParameters(timep,physicalp,solverp,exportp)

airfoil_case = Airfoil(meshp,simparams,sprob) ```

Now, the objective function is defined. it only takes one argument [CD,CL], then you can define all the keywords you want. The boundary conditions are defined as -dJ/dCDCL

julia function J(CDCL; CLtarget=0.75) CD,CL=CDCL return CD/CL end

Now we define the adjoint solver, where there are many customizable options, see in src/ParametersAdj/ParametersAdj.jl ```julia adj_solver = AdjSolver(δ=0.0001)

```

Then, we solve the problem. (:unsteady, :steady) means that the primal flow is solved as unsteady and the adjoint is solve as steady.

```julia adjointairfoilproblem = AdjointProblem( rbfd,airfoilcase,adjsolver, (:unsteady, :steady), J )

```

Adjoint Simulation

Look at the example: EX_M.jl

Finite Difference

Look at the example: EX_FD.jl

Installation

The package has not been registered yet so you can install it as: julia using Pkg Pkg.add(url="https://github.com/carlodev/VMSAdjoint.jl")

Packages recommendation

https://github.com/carlodev/SegregatedVMSSolver.jl#Update-deps https://github.com/carlodev/AirfoilTools.jl#master

They will published soon - they are still under development

Note

The package has been developed having in mind the parallelization, which is going to be implemented.

Contributing

It is a collaborative project open to contributions. You can: - Open a new issue - Contact the project administator - Open a PR with the contribution