Stokes Repository

Code to solve the Stokes equations using boundary integral equations.

Features

• confined flows, uses Power-Miranda formulation and an FMM to rapidly compute sums
• periodic domains, uses spectral Ewald to rapidly compute infinte sums
• special quadrature for on-surface evaluation of single-layer potential as well as near-surface evaluation of single- and double-layer potentials

Compilation instructions

In addition to this repository you will need the tool for Legendre polynomials in https://github.com/ludvigak/legtools and the fast multiplication methods in https://github.com/lukasbystricky/FastTools2D. Compilation instructions for the latter repository are provided in its README, however the following sequence has been tested on Ubuntu 16.04 with Matlab 2017a as well as on Ubuntu 18.04 with Matlab 2021a:

## clone repositories
git clone https://github.com/ludvigak/legtools
git clone https://github.com/lukasbystricky/FastTools2D.git
git clone https://github.com/lukasbystricky/Stokes2D.git

## compile periodic spectral Ewald
cd FastTools2D/PeriodicEwald/src/build
cmake ..
make

## compile FMM if desired
## NB: on Mac, Matlab mex requires the intel compilers
## The makefiles will need to be edited!
cd FastTools2D/FMM/src/StokesDLP
make
cd ../StokesSLP
make

## compile special quadrature routines
cd ../../../Stokes2D/src/build
cmake ..
make
cd ../..

Start Matlab and run initpaths.m to initialize the proper paths. To test the spectral Ewald and special quadrature run demo_periodic_pouseille_flow. With 10 panels on each wall, you should acheive around 14 digits of accuracy everywhere in the domain.

To test the FMM, run demo_taylor_couette.m. With 10 panels on the outer wall and 5 panels on the inner wall you should see 12 digits of accuracy everywhere.

To do

• check OpenMP timings
• RCIP for corner treatment
• Navier-slip boundary conditions, adjoint double-layer potential