On the use of reverse Brownian motion to accelerate hybrid simulations

Abstract

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

Stochastic Pore Collapse Models in Granular Materials

“…We will use Eqn. (9) to determine σ ξ = σ ξ ( τ ), the noise strength in our stochastic flow rule (2).…”

“…It describes the temporal evolution of the strain probability of deformation, p(ε ij , t|ε 0 ij , t 0 ). This equation can be solved numerically using reverse Brownian motion locally in Langevin equivalent [9].…”

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

“…(26), represents the variance of the distribution of F which was hypothesized to decay with time since the passage of the first shock, i. e. t in Eq. (28). From the mesoscale simulation, the variance of F over the RVE previously described was tracked through time.…”

“…Such mesoscale calculations are expected to reveal that the true functional form is more complicated than what was postulated in Eq. (28). On the other hand, the mesoscale simulations referred to here were only carried out for a short amount of time, and longer simulation times will reveal more information about the shape of the decay.…”

“…Tantalizingly close numerical methods can be found within the granular flow and droplet laden flow communities, but it will take time to repurpose these methods for heterogeneous solid explosives. Progress is also being made in stochastic computational modelling that may be relevant to the current work . Finally, dissipative particle dynamics (DPD) and other DPD variants have been used to run large three‐dimensional particle simulations in order to bridge the gap between fluctuations at the molecular level and the continuum.…”