Zihao Yang

Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures

In this paper, we perform a second-order two-scale analysis and introduce a numerical algorithm for the damped wave equations of composite materials with a quasi-periodic structure. Firstly, second-order two-scale asymptotic expansion solutions for these problems are constructed by a multiscale asymptotic analysis. In addition, we explain the importance of the second-order two-scale solutions by the error analysis in the pointwise sense. Moreover, explicit convergence rates of these second-order two-scale solutions are obtained in the integral sense. Then a second-order two-scale numerical method based on a Newmark scheme is presented to solve these multiscale problems. Finally, some numerical examples show the effectiveness and efficiency of the multiscale numerical method we proposed.

Second-order two-scale computational method for damped dynamic thermo-mechanical problems of quasi-periodic composite materials

Abstract In this paper, a novel second-order two-scale (SOTS) analysis method and related numerical algorithm are developed for damped dynamic thermo-mechanical problems of quasi-periodic composite materials. The formal SOTS solutions for these problems are constructed by the multiscale asymptotic analysis. Then we theoretically explain the importance of the SOTS solutions by the error analysis in the pointwise sense. Furthermore, the convergence result with an explicit rate for the SOTS solutions is obtained in the integral sense. In addition, a SOTS numerical algorithm is proposed to solve these problems effectively. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on asymptotic homogenization method. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing SOTS solutions. Furthermore, the error estimates for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

Multiscale analysis and computation for coupled conduction, convection and radiation heat transfer problem in porous materials

Abstract This paper discusses the multiscale analysis and numerical algorithms for coupled conduction, convection and radiation heat transfer problem in periodic porous materials. First, the multiscale asymptotic expansion of the solution for the coupled problem is presented, and high-order correctors are constructed. Then, error estimates and their proofs will be given on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale method are introduced and some numerical results are given in detail. The numerical tests demonstrate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper.

High-order three-scale computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales

Abstract This study develops a novel high-order three-scale (HOTS) computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales. The heterogeneities of the composites are taken into account by periodic distributions of unit cells on the mesoscale and microscale. Firstly, the multiscale asymptotic analysis for these multiscale problems is given detailedly. Based on the above-mentioned analysis, the new unified micro-meso-macro HOTS approximate solutions are successfully constructed for these multiscale problems. Two classes of auxiliary cell functions are established on the mesoscale and microscale. Then, the error analyses for the conventional two-scale solutions, low-order three-scale (LOTS) solutions and HOTS solutions are obtained in the pointwise sense, which illustrate the necessity of developing HOTS solutions for simulating the heat conduction behaviors of composite structures with multiple periodic configurations. Furthermore, the corresponding HOTS numerical algorithm based on finite element method (FEM) is brought forward in details. Finally, some numerical examples are presented to verify the feasibility and validity of our HOTS computational method. In this paper, a unified three-scale computational framework is established for heat conduction problems of axisymmetric composite structures with multiple spatial scales.