Abstract This paper presents a framework for the application of the discontinuous Galerkin(DG) finite element method to the multi-physics simulation of the solid thermal deformation interacting with incompressible flow problems in two-dimensions. Recent applications of the DG method are primarily for thermoelastic problems in a solid domain or fluid-structure interaction problems without heat transfer. Based on a recently published conjugate heat transfer solver, the incompressible Navier-Stokes equation, the fluid advection-diffusion equation, the Boussinesq term, the solid heat equation and the solid linear elastic equation are solved using an explicit DG formulation. A Dirichlet-Neumann partitioning strategy has been implemented to achieve the data exchange process via the numerical flux computed at interface quadrature points in the fluid-solid interface. Formal hp convergence studies employing the method of manufactured solutions demonstrate that the expected order of accuracy is achieved for each solver. The algorithm is then further validated against several existing benchmark cases including the in-plane loaded square, the Timoshenko Beam, the laminated beam subject to thermal-loads and the lid-driven cavity with a flexible bottom wall. The computational effort demonstrates that for all cases the highest order accurate algorithm has several magnitudes lower error than the second-order schemes for a given computational effort. It is a strong justification for the development of such high order discretisations. The solver can be employed to predict thermal deformation of a structure due to convective and conductive heat transfer at low Mach, such as chip deformation on a printed circuit board, wave-guide structure optimization, thermoelectric cooler simulation, and optics mounting method verification.

中文翻译：

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一种模拟不可压缩流体-热-结构相互作用问题的高阶不连续伽辽金方法

摘要 本文提出了一个框架，用于将不连续伽辽金 (DG) 有限元方法应用于固体热变形与二维不可压缩流动问题相互作用的多物理场模拟。DG 方法的最新应用主要是解决固体域中的热弹性问题或没有传热的流固耦合问题。基于最近发布的共轭传热求解器，使用显式 DG 公式求解不可压缩的纳维-斯托克斯方程、流体对流-扩散方程、Boussinesq 项、固体热方程和固体线弹性方程。已实施 Dirichlet-Neumann 分区策略，以通过在流固界面中的界面正交点处计算的数值通量来实现数据交换过程。采用制造解决方案方法的正式 hp 收敛研究表明，每个求解器都达到了预期的精度顺序。然后，该算法针对几个现有的基准案例进行了进一步验证，包括面内加载的正方形、Timoshenko 梁、承受热载荷的层压梁和具有柔性底壁的盖驱动腔。计算工作表明，对于所有情况，对于给定的计算工作，最高阶精确算法的误差比二阶方案低几个数量级。这是发展这种高阶离散化的有力理由。该求解器可用于预测由于低马赫数下的对流和传导热传递引起的结构热变形，例如印刷电路板上的芯片变形、波导结构优化、热电冷却器模拟和光学安装方法验证。