Add EKIN to Walberla branch

[RudolfWeeber]

Structure, LB coupling

• EK and LB can each be used independently but also in combination
• If used in combination, the LB velocity field is passed into EK, and EK adds to the LB force field
• To allow for this, they should share the Walberla Blockforest (the data structure that handles the domain decomposition and field storage in Walberla)
• To this end, a Lattice component is introduced:
  • Owns the Walberla-Blockforest
  • Parameters: number of cells per direction, number of blocks per direction per mpi rank, time step
  • Is passed as argument to the LB and EK upon their instanceiation
• EK und LB get a shared pointer to the block forest from the lattice component

EK

Fields

$n$ = number of species, $r$ = number o reactions

• $n$ densities
• $n$ fluxes
• 1 total charge
• 1 electrostatic potential
• reference to LB velocity and force fields (as BlockDataId)

Parameter:

• $n$ * diffusion coefficients
• $n$ charges (valencies)
• kT
• $r \times n$ * stoich. coefficients
• $r \times n$ Reaction orders
• $r$ * reactionrates

Kernel (in order of execution)

• Calculate total charge from per species densities and valencies
• FFT-Solver (from Walberla in combination with pfft)
• Flux- and LB-force computation (executed for every species, can contain thermal fluctuations)
• $r$ Reactions (adds source/sink terms to fluxes)
• Boundary conditions
• Continuity equation (for each species)

Sll kernels except the FFT solver for the Poisson eqn are generated using PyStencils/PyStenilcs_Walberla

Reaction kernels

• Seperate kernels will be generated for the number of reactants.
• Educts and Prudcuts will not have to be considerd separately. This is hanlded by the sign of the stoich. coeff.
• There will be kernels from 1 to 5 reacting species.

Next steps

• Write a Python script generating all necessary kernels
• Implement the Lattice component holding the BlockForest and lattice, pull out the block forest from the LB base class (LBWalberlaImpl)
• Create the Python interface for the Lattice component
• Write the EK base class

[itischler]

first ek kernel generator added here
boundary and electrostatics kernels still to be done

[jngrad]

@reinaual's walberla_ekin_scriptinterface branch has been merged into the walberla branch.

• ESPResSo 4.3-dev now has:
  • an EK class that can be used alone or together with the LB class
  • electrokinetic solvers, kernels for bulk and indexed reactions
  • density and flux boundaries that can be created from a shape or on a per-node basis
• code duplication between LBWalberlaImpl and EKinWalberlaImpl has been factored out
• the LB and EK classes for VTK writers have been merged into one common interface
• the EK code (excluding generated kernels) is 98% covered by integration tests
• the user guide chapter on ekin has been restored and updated accordingly

[jngrad]

Last remaining tasks:

• EK coupling to LB with thermal fluctuations
  • blocked due to how the RNG is implemented in lbmpy
• EK unit conversions between python interface and C++ class
• EK unit conversions in VTK files
• C++ unit tests for EK
• checkpointing