Langevin Particle: A Self-Adaptive Lagrangian Primitive for Flow Simulation Enhancement

Abstract

We develop a new Lagrangian primitive, named Langevin particle, to incorporate turbulent flow details in fluid simulation. A group of the particles are distributed inside the simulation domain based on a turbulence energy model with turbulence viscosity. A particle in particular moves obeying the generalized Langevin equation, a well known stochastic differential equation that describes the particle's motion as a random Markov process. The resultant particle trajectory shows self-adapted fluctuation in accordance to the turbulence energy, while following the global flow dynamics. We then feed back Langevin forces to the simulation based on the stochastic trajectory, which drive the flow with necessary turbulence. The new hybrid flow simulation method features nonrestricted particle evolution requiring minimal extra manipulation after initiation. The flow turbulence is easily controlled and the total computational overhead of enhancement is minimal based on typical fluid solvers.