发表机构
Laboratoire de Mécanique des Solides (LMS), École Polytechnique, CNRS UMR 7649, Institut Polytechnique de Paris（固体力学实验室（LMS），巴黎综合理工学院，法国国家科学研究中心联合研究单位 7649，巴黎理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出谱伽辽金框架求解有限域非线性瞬态热传导，通过线性参考问题与模态ODE实现高效GPU并行，以小于1%误差和227倍加速复现有限元结果，并显著影响激光加工指标。
AI 中文摘要
准确模拟非均匀温度场的时间演化，需要解决热方程中因温度相关的热物理性质、相变潜热以及局部热源/热汇而产生的强非线性问题。在本工作中，我们提出了一种谱伽辽金（SG）框架，用于求解有限域内的完全非线性瞬态热方程，以显著更低的计算成本达到高保真有限元（FE）模拟的精度。热方程被重新表述为一个具有恒定热物理性质和残余强迫项的线性参考问题。求解参考问题提供了一个完整的三维标准正交三角基，其伽辽金投影将热方程简化为一系列时间上的模态常微分方程（ODE）；参考算子在模态基下是对角的，对于固定的非线性强迫项，可实现独立的模态更新。这些常微分方程可以使用指数时间差分进行积分，并针对非线性进行迭代校正。SG方法消除了有限元方法所需的全局求解，并且其使用结构化网格允许高效的GPU并行化。应用于快速激光-金属相互作用时，SG求解器以小于1%的相对误差重现了高保真有限元温度场，同时实现了227倍的GPU运行时间加速。应用于零件尺度激光扫描研究[Ramani等人，增材制造52（2022）102643]时，该方法表明考虑蒸发和潜热使其提出的加工指标减少了一半以上。SG热求解器的源代码及一些示例可在Apache 2.0许可下于该https URL获取。
英文摘要
Accurately modelling the temporal evolution of heterogeneous temperature fields requires resolving strong nonlinearities in the heat equation arising from temperature-dependent thermophysical properties, latent heats of transformation and any local heat sources/sinks. In this work, we present a spectral Galerkin (SG) framework to solve the fully nonlinear transient heat equation in finite domains to attain the accuracy of high-fidelity finite element (FE) simulations at considerably lower computational cost. The heat equation is reformulated into a linear reference problem with constant thermophysical properties and residual forcing terms. Solving the reference problem provides a complete three-dimensional orthonormal trigonometric basis, whose Galerkin projection reduces the heat equation to a set of modal ordinary differential equations (ODEs) in time; the reference operator is diagonal in the modal basis, and results in independent modal updates for a fixed nonlinear forcing. These ODEs can be integrated using exponential time differencing and iteratively corrected for nonlinearities. The SG method eliminates the global solve required by FE methods, and its use of structured grids allows efficient GPU parallelization. Applied to rapid laser-metal interactions, the SG solver reproduces high-fidelity FE temperature fields with less than 1% relative error while achieving 227-fold faster GPU runtimes. Applied to a part-scale laser scanning study [Ramani et al., Additive Manufacturing 52 (2022) 102643], the method shows that accounting for evaporation and latent heat more than halves their proposed processing metric. The source code of the SG heat solver and some worked examples are available at https://github.com/manasvupadhyay/spectral_galerkin_heat under the Apache 2.0 license.
Commentspreprint, 30 pages, 1 algorithm, 1 link to source code, 15 figures, 3 tables
