  We present a computational method for solving the coupled problem of chemical
transport in a fluid (blood) with binding/unbinding of the chemical to/from
cellular (platelet) surfaces in contact with the fluid, and with transport of
the chemical on the cellular surfaces. The overall framework is the Augmented
Forcing Point Method (AFM) (\emph{L. Yao and A.L. Fogelson, Simulations of
chemical transport and reaction in a suspension of cells I: An augmented
forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for
solving fluid-phase transport in a region outside of a collection of cells
suspended in the fluid. We introduce a novel Radial Basis Function-Finite
Difference (RBF-FD) method to solve reaction-diffusion equations on the surface
of each of a collection of 2D stationary platelets suspended in blood.
Parametric RBFs are used to represent the geometry of the platelets and give
accurate geometric information needed for the RBF-FD method. Symmetric
Hermite-RBF interpolants are used for enforcing the boundary conditions on the
fluid-phase chemical concentration, and their use removes a significant
limitation of the original AFM. The efficacy of the new methods are shown
through a series of numerical experiments; in particular, second order
convergence for the coupled problem is demonstrated.
