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An optimally-coupled multi-time stepping method for transient heat conduction simulation for additive manufacturing
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-04-21 , DOI: 10.1016/j.cma.2021.113825
Lin Cheng , Gregory J. Wagner

With growing application of additive manufacturing (AM) in industry, simulation of transient heat conduction during the AM process has drawn increasing attention. However, detailed simulation with acceptable accuracy is extremely time consuming because of the large range of time scales involved in the problem. In this work, a multi-time stepping method using different timesteps in multiple subdomains is developed to accelerate transient heat conduction simulation. A Dirichlet–Robin iterative coupling scheme is proposed to enforce continuity at the interfaces between different subdomains. This allows numerical stability of the multi-timestep​ model, even with disparate materials or meshes on either side of the subdomain interfaces. Specifically, an optimal approximation for the Schur complement matrix is derived using a one-dimensional (1D) model, which avoids the instabilities encountered when using a Dirichlet–Neumann coupling formulation and allows convergence of the iterative coupling scheme in only one iteration at each timestep. Several numerical examples are studied to evaluate the stability, convergence and performance of the method. It is found that the proposed method is robust and stable for all choices of material parameters, unlike the conventional Dirichlet–Neumann coupling scheme. To demonstrate the use of the method for AM, a simulation representative of a single laser track is performed and compared with line heat source model approach. It is found that the proposed method not only accelerates the simulation by a factor of more than 100, but gives very good accuracy for temperature in the melt pool region.



中文翻译:

增材制造瞬态热传导仿真的最优耦合多步法

随着增材制造(AM)在工业中的应用不断增长,在制造过程中模拟瞬态导热增材制造过程引起了越来越多的关注。但是,由于问题涉及的时间范围很大,因此以可接受的精度进行详细的模拟非常耗时。在这项工作中,开发了在多个子域中使用不同时间步长的多时间步长方法,以加速瞬态热传导仿真。提出了一种Dirichlet-Robin迭代耦合方案,以在不同子域之间的接口处实现连续性。即使在子域界面的两侧使用不同的材料或网格,这也可以实现多时间步长模型的数值稳定性。具体来说,使用一维(1D)模型得出Schur补矩阵的最佳近似值,这避免了使用Dirichlet-Neumann耦合公式时遇到的不稳定性,并且允许迭代耦合方案在每个时间步仅一次迭代即可收敛。研究了几个数值示例,以评估该方法的稳定性,收敛性和性能。发现,与传统的Dirichlet-Neumann耦合方案不同,所提出的方法对于所有材料参数选择均具有鲁棒性和稳定性。为了演示该方法在AM中的使用,执行了一个代表单个激光轨迹的仿真,并将其与线热源模型方法进行了比较。发现所提出的方法不仅使模拟加速了100倍以上,而且对熔池区域的温度也提供了非常好的精度。研究了几个数值示例,以评估该方法的稳定性,收敛性和性能。发现,与传统的Dirichlet-Neumann耦合方案不同,所提出的方法对于所有材料参数选择均具有鲁棒性和稳定性。为了演示该方法在AM中的使用,执行了一个代表单个激光轨迹的仿真,并将其与线热源模型方法进行了比较。发现所提出的方法不仅使模拟加速了100倍以上,而且对熔池区域的温度也提供了非常好的精度。研究了几个数值示例,以评估该方法的稳定性,收敛性和性能。发现,与传统的Dirichlet-Neumann耦合方案不同,所提出的方法对于所有材料参数选择均具有鲁棒性和稳定性。为了演示该方法在AM中的使用,执行了一个代表单个激光轨迹的仿真,并将其与线热源模型方法进行了比较。发现所提出的方法不仅使模拟加速了100倍以上,而且对熔池区域的温度也提供了非常好的精度。与传统的Dirichlet-Neumann耦合方案不同。为了演示该方法在AM中的使用,执行了一个代表单个激光轨迹的仿真,并将其与线热源模型方法进行了比较。发现所提出的方法不仅使模拟加速了100倍以上,而且对熔池区域的温度也提供了非常好的精度。与传统的Dirichlet-Neumann耦合方案不同。为了演示该方法在AM中的使用,执行了一个代表单个激光轨迹的仿真,并将其与线热源模型方法进行了比较。发现所提出的方法不仅使模拟加速了100倍以上,而且对熔池区域的温度也提供了非常好的精度。

更新日期:2021-04-22
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