| Home > Publications > Reports > Numerical Analysis and Applied Mathematics (TW) |
TW 476
Pieter Van Leemput, Christophe Vandekerckhove, Wim Vanroose, and Dirk Roose
Accuracy of hybrid lattice Boltzmann/finite difference schemes for reaction-diffusion systems
Abstract
In this article we construct a hybrid model by spatially coupling a lattice Boltzmann equation (LBE) to a finite difference discretization of the corresponding partial differential equation (PDE) for reaction-diffusion systems. Because the LBE has more variables (the particle distribution functions) than the PDE (only the particle density), we have a one-to-many mapping problem from the PDE to the LBE domain at the interface. We perform this mapping using either results from the Chapman-Enskog expansion or a point-wise iterative scheme that approximates these analytical relations numerically. Most importantly, we show that the global spatial discretization error of the hybrid model is one order less accurate than the local error made at the interface. We derive closed expressions for the spatial discretization error at steady state and verify them numerically for several examples on the one-dimensional domain.
report.pdf (274K) / mailto: P. Van Leemput