A particle-based method called multi-particle collision (MPC) dynamics is considered, and the shear viscosity is calculated theoretically. As part of the particle-based mechanism, velocities of particles change due to collisions and due to an applied external force used to create flow. The system's temperature increases due to the external force, and a thermostat is used to remove this excess temperature so as to maintain constant temperature (isothermal) flow conditions. A theoretical expression for the shear viscosity is derived and compared to existing viscosity expressions.
Additionally, results for MPC flow through a local constriction are assessed. The novelty of the numerical results in this Thesis come from using a local thermostat rather than a global thermostat that had been used in the past.