An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications

Abstract

A concurrent multiscale method is developed to model time-dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved. Ensuring this energetic consistency among scales enables the implementation of high fidelity physics-based models at critical locations within the coarse-scale to temporally and spatially resolve highly complex and localized phenomena. To achieve this, only Neumann boundary conditions are applied over the fine scale domain, ensuring a conservative formulation. The coarse-scale solution is used to reconstruct these Neumann boundary conditions on the fine scale, which are then used to evolve a separate system of governing equations. The results on the fine scale are then sent back to the coarse scale through an energy-based homogenization scheme. Transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness, including the coupling of a phase field model at the fine scale to a coarse-scale heat equation.

Multiscale Modeling for Food Drying: State of the Art

“…One‐way coupled models for multiphase flow in porous media (Lunati & Jenny, ) and multiscale transport in heterogeneous porous media have been published. In addition, two‐way coupled models exist on unsaturated soils (Carr & Turner, ) and heterogeneous heat transfer in phase transition application (Lin, Smith, Liu, & Wagner, ). Considerable work has been done on soft matter for one‐way coupled models for deformation (Aregawi et al., ), pore transport (Ryan & Tartakovsky, ), gas transport (Ho et al., ; Ho, Verboven, Verlinden, & Nicolaï, ), general transport (Ho, Verboven, Verlinden, Herremans, & Nicolaï, ), and porous media (Delele et al., ).…”

“…Lin et al. () constructed a HMM‐inspired framework for heterogeneous heat transfer and phase transition applications. They coupled a single state variable of temperature within the concurrent framework.…”

“…Dirichlet is quite a straight‐forward approach and is commonly used in many different modeling applications. A Neumann condition also appears regularly in the literature and can be used to create an energy‐consistent model between a microscale and a macroscale (Lin et al., ). Other traditional boundary conditions such as Cauchy or Robin conditions exist.…”

Benchmark modeling and 3D applications of solidification and macro-segregation based on an operator-splitting and fully decoupled scheme with term-wise matrix assembly

“…Other methods like the molecular dynamics simulation [27,28] is also used to study solidification. The enthalpy-porosity method [29] and the phase field method [30,31,32] attracted a lot of research attention as the mesh-based methods. They not only circumvent the difficulties of interface reconstruction but also maintain the reproduction of physical properties.…”

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

“…Heat transfer in heterogeneous media widely exist in many fields. Numerical simulation is an efficient method for solving the common heat transfer problem, and heat transfer problem in heterogeneous media has been investigated with various numerical methods, such as meshless method [1], discrete element method [2], finite element method [3][4][5][6] and lattice Boltzmann method [7][8][9].…”