Bingham fluid simulations using a physically consistent particle method

The Bingham fluid simulation model was constructed and validated using a physically consistent particle method, i.e., the Moving Particle Hydrodynamics (MPH) method. When a discrete particle system satisfies the fundamental laws of physics, the method is asserted as physically consistent. Since Bingham fluids sometimes show solid-like behaviors, linear and angular momentum conservation is especially important. These features are naturally satisfied in the MPH method. To model the Bingham feature, the viscosity of the fluid was varied to express the stress-strain rate relation. Since the solid-like part, where the stress does not exceed the yield stress, was modeled with very large viscosity, the implicit velocity calculation was introduced so as to avoid the restriction of the time step width with respect to the diffusion number. As a result, the present model could express the stopping and solid-like behaviors, which are characteristics of Bingham fluids. The proposed method was verified and validated, and its capability was demonstrated through calculations of the two-dimensional Poiseuille flow of a Bingham plastic fluid and the three-dimensional dam-break flow of a Bingham pseudoplastic fluid by comparing those computed results to theory and experiment.