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TW 509
Giovanni Samaey
Alternative patch boundary conditions for the heterogeneous multiscale simulation of hyperbolic homogenization problems
Abstract
For problems where a macroscopic conservation law is known to exist, but only a microscopic model is available, E and Engquist proposed a so-called \emph{heterogeneous multiscale method} (HMM). In this method, the macroscopic flux (for which no explicit formula is available) is estimated from appropriately initialized microscopic simulations, which are performed in small patches around the macroscopic grid points, subject to periodic boundary conditions. In this paper, we investigate the effect of alternative (arbitrary) boundary conditions on the accuracy and efficiency of the flux computations. We analyze the artifacts that are introduced when using a no-flux boundary condition in the case of one-dimensional transport homogenization problems, and derive a relation between the required size of the patch in the space domain and the length of the associated microscopic simulation. A detailed comparison with the original HMM formulation shows that, as soon as the homogenization problem is not periodic on the small scale, the use of periodic boundary conditions offers no advantage, compared to using arbitrary boundary conditions.
report.pdf (3.6M) / mailto: G. Samaey