Convergence of stochastic cellular automation to Burger's equation: fluctuations and stability
Physica D - Progress in Chaotic Dynamics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Journal of Computational Physics
Multiscale finite-difference-diffusion-Monte-Carlo method for simulating dendritic solidification
Journal of Computational Physics
Algorithm refinement for stochastic partial differential equations: I. linear diffusion
Journal of Computational Physics
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth
Journal of Computational Physics
A hybrid continuum/particle approach for modeling subsonic, rarefied gas flows
Journal of Computational Physics
Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics
Journal of Computational Physics
Algorithm refinement for stochastic partial differential equations: II. Correlated systems
Journal of Computational Physics
A hybrid particle-continuum method applied to shock waves
Journal of Computational Physics
Hybrid atomistic-continuum method for the simulation of dense fluid flows
Journal of Computational Physics
Uncertainty quantification for systems of conservation laws
Journal of Computational Physics
Adaptive mesh refinement for stochastic reaction-diffusion processes
Journal of Computational Physics
Original Articles: Meshfree method for fluctuating hydrodynamics
Mathematics and Computers in Simulation
Noise propagation in hybrid models of nonlinear systems: The Ginzburg-Landau equation
Journal of Computational Physics
Hi-index | 31.46 |
In this paper, we develop an algorithm refinement (AR) scheme for an excluded random walk model whose mean field behavior is given by the viscous Burgers' equation. AR hybrids use the adaptive mesh refinement framework to model a system using a molecular algorithm where desired while allowing a computationally faster continuum representation to be used in the remainder of the domain. The focus in this paper is the role of fluctuations on the dynamics. In particular, we demonstrate that it is necessary to include a stochastic forcing term in Burgers' equation to accurately capture the correct behavior of the system. The conclusion we draw from this study is that the fidelity of multiscale methods that couple disparate algorithms depends on the consistent modeling of fluctuations in each algorithm and on a coupling, such as algorithm refinement, that preserves this consistency.