A Duhamel approach for the Langevin equations with holonomic constraints

To simulate polymer flows in microscale environments we have developed a numerical method that couples stochastic particle dynamics with an efficient incompressible Navier-Stokes solver. Here, we examine properties of the particle solver alone. We derive a Duhamel-form stochastic particle method for freely jointed polymers and demonstrate that it achieves 2-order weak convergence and 3/2-order strong convergence with holonomic constraints. For time steps approaching the 1/gamma relaxation time, our method displays greatly enhanced stability relative to comparable solvers based on linearised dynamics. Under these same conditions, our method has solution errors that are approximately six orders of magnitude smaller than that for the linearised algorithm.