Introduction to Multiscale Mathematical Modeling by Grigory Panasenko

Author:Grigory Panasenko
Language: eng
Format: epub
Publisher: World Scientific Publishing Co. Pte. Ltd
Published: 2022-08-15T00:00:00+00:00

we see that asymptotic approximation (3.3.4) satisfies exactly the boundary and initial conditions.

Problem (3.3.13)–(3.3.15) is called homogenized problem.

In the following section, we prove that

Thus, the equivalent homogeneity hypothesis is justified in this example and the formulas for the macroscopic effective coefficients are 〈c(ξ)〉 for the effective heat capacity and the effective conductivity.

Note that in the multi-dimensional case, the algorithm for the computation of the effective coefficients is more complicated (see the following). For piecewise smooth coefficients, this analysis should be completed by a special treatment of the interface conditions (3.2.3), (3.2.4) adding the corresponding interface conditions for equation (3.3.6). The algorithm for the computation of effective coefficients is left without changes.

The heat equation (3.3.1) also describes some other physical processes, such as diffusion and flows in porous media.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.