  We develop a numerical a framework to study phoretic particle dynamics in two
dimensions. The particles are modeled as chemically active rigid circles, which
can emit or absorb a solute into surrounding fluid. The interaction between
particles and solute induces a slip flow on particle surfaces, and the solute
is advected by the fluid flow and diffuses with a constant diffusivity. The
fluid-structure interaction is resolved by a boundary integral method
accelerated by Ewald-like decomposition. The sharp resolution of moving
boundaries for solute kinetics is performed thanks to an overlapping mesh
method. The framework is validated separately for the Stokes problem and the
advection--diffusion problem, reaching relatively high order of accuracy.
Moreover, we employ the framework to more general problems, including particles
in nearly infinite domain and straight channels, and multiparticle motions.
