  Most biological fluids are viscoelastic, meaning that they have elastic
properties in addition to the dissipative properties found in Newtonian fluids.
Computational models can help us understand viscoelastic flow, but are often
limited in how they deal with complex flow geometries and suspended particles.
Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can
handle arbitrarily-shaped fixed and moving boundary conditions, which makes it
ideally suited for the simulation of confined colloidal suspensions. We
validate our method using several standard rheological setups, and additionally
study a single sedimenting colloid, also finding good agreement with
literature. Our approach can readily be extended to constitutive equations
other than Oldroyd-B. This flexibility and the handling of complex boundaries
holds promise for the study of microswimmers in viscoelastic fluids.
