Multiscale Seamless-Domain Method for Nonperiodic Fields: Nonlinear Heat Conduction Analysis

Abstract

A multiscale numerical solver called the seamless-domain method (SDM) is used in linear heat conduction analysis of nonperiodic simulated fields. The practical feasibility of the SDM has been verified for use with periodic fields but has not previously been verified for use with nonperiodic fields. In this paper, we illustrate the mathematical framework of the SDM and the associated error factors in detail. We then analyze a homogeneous temperature field using the SDM, the standard finite difference method, and the conventional domain decomposition method (DDM) to compare the convergence properties of these methods. In addition, to compare their computational accuracies and time requirements, we also simulated a nonperiodic temperature field with a nonuniform thermal conductivity distribution using the three methods. The accuracy of the SDM is very high and is approximately equivalent to that of the DDM. The mean temperature error is less than 0.02% of the maximum temperature in the simulated field. The total central processing unit (CPU) times required for the analyses using the most efficient SDM model and the DDM model represent 13% and 17% of that of the finite difference model, respectively.

Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

“…State-of-the-art papers devoted to the review and classification of multiscale methods developed for the heat transfer problem are present in the literature [ 25 , 26 , 27 ]. The main distinction refers to the analysis scale [ 27 ]; therefore, one can distinguish: The microscale modeling using molecular dynamics (MD) with the motion analysis of every single atom/molecule in the domain [ 28 , 29 ]; The particle-based mesoscopic modeling based on a coarse-grained analysis, e.g., Monte Carlo method, lattice Boltzmann method [ 30 ]; The macroscale modeling with the assumption of the continuum of the domain [ 2 , 13 , 31 , 32 ]. …”

“…In order to avoid the problem of the excessively large amount of the information obtained in the direct composite analyses at any scale, a number of hybrid and multiscale methods are used for the heat transfer problem [ 27 , 28 , 30 , 31 ]. They can be classified in a manifold manner.…”

“…In the case of micro- and mesoscale analysis, we arbitrarily selected the most representative methods. For an extensive review of these, we refer the reader to [ 27 , 28 , 30 , 31 ]. In the case of the macroscale modeling, the description is slightly different.…”

“…In [ 13 , 31 ], the multiscale seamless-domain method (SDM) is presented. It has some similarities to both the computational homogenization and the multiscale finite-element method used in this paper.…”