  Phoretic colloids self-propel thanks to surface flows generated in response
to surface gradients (thermal, electrical, or chemical), that are self-induced
and/or generated by other particles. Here we present a scalable and versatile
framework to model chemical and hydrodynamic interactions in large suspensions
of arbitrarily shaped phoretic particles, accounting for thermal fluctuations
at all Damkholer numbers. Our approach, inspired by the Boundary Element Method
(BEM), employs second-layer formulations, regularised kernels and a grid
optimisation strategy to solve the coupled Laplace-Stokes equations with
reasonable accuracy at a fraction of the computational cost associated with
BEM. As demonstrated by our large-scale simulations, the capabilities of our
method enable the exploration of new physical phenomena that, to our knowledge,
have not been previously addressed by numerical simulations.
