A Multiscale Method for Coupled Steady-State Heat Conduction and Radiative Transfer Equations in Composite Materials

The prediction of coupled conduction-radiation heat transfer in periodic composite materials is important for the application of the materials in high-temperature environment. Homogenization method is widely used for the heat conduction problem, but the coupled radiative transfer equation is seldom studied. In this work, the homogenization method is extended to the coupled conduction-radiation heat transfer in composite materials with periodic microscopic structures, in which both the heat conduction and radiative transfer equations are analyzed. The homogenized equations are obtained for the macroscopic heat transfer. The unit cell problems are also derived, which provide the effective coefficients for the homogenized equations and the local temperature and radiation corrections. The second-order asymptotic expansion of the temperature field and first-order asymptotic expansion of the radiative intensity field are established. A multiscale numerical algorithm is proposed to simulate the coupled conduction-radiation heat transfer in materials doped with isotropic or anisotropic particles. According to the numerical examples in this work, comparing with the fully-resolved simulations, the errors of the multiscale model are less than 13% for the temperature and less than 8% for the radiation. The computational time can be reduced from more than 300 hours to less than 30 minutes. Therefore, the proposed multiscale method can maintain the accuracy of the calculation and significantly improve the computational efficiency. It can provide both the average temperature and radiation for engineering utilizations and the local information corresponding to the microstructure of the composite materials.

Finite difference forward modelling across the Tyrrhenian basin

<p>Strong lateral variations in medium properties affect the response of seismic wavefields. The Tyrrhenian Sea is ideally suited to explore these effects in a mixed continental-oceanic crust that comprises magmatic systems. The study aims at investigating the effects of crustal thinning and sedimentary layers on wave propagation, especially the reverberating (e.g., Lg) phases, across the oceanic basin. We model regional seismograms (600-800 km) using the software tool OpenSWPC (Maeda et al., 2017, EPS) based on the finite difference simulation of the wave equation. The code simulates the seismic wave propagation in heterogeneous viscoelastic media including the statistical velocity fluctuations as well as heterogeneous topography, typical of mixed settings. This approach allows to evaluate the role of interfaces and layer thicknesses on phase arrivals and direct and coda attenuation measurements. The results are compared with previous simulations of the radiative-transfer equations. They provide an improved understanding of the complex wave attenuation and energy leakage in the mantle characterizing the southern part of the Tyrrhenian Sea and the Italian peninsula. The forward modelling is to be embedded in future applications of attenuation, absorption and scattering tomography performed with MuRAT (the Multi-Resolution Attenuation Tomography code – De Siena et al. 2014, JVGR) available at https://github.com/LucaDeSiena/MuRAT.</p>