论文标题
使用广义BousSinesQ模型进行加热材料处理的多数型后验误差控制
Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model
论文作者
论文摘要
在这项工作中，我们为广义的BousSinesQ模型开发了后验误差控制，其中导热率和粘度依赖于温度。在其中，固定的Navier-Stokes方程与固定热方程式结合在一起。耦合问题以单片方式建模和解决。重点是使用双重加权残差方法进行多数面向误差估计，其中利用伴随问题来获得相对于多个目标功能的灵敏度度量。借助弱公式中的合法性分区实现了错误定位，这对于耦合问题特别方便，就像我们手头一样。误差指标用于采用自适应算法，这些算法通过几个数值测试（例如一个基准测试）和两个由激光材料处理动机进行的实验证实。在其中，咨询了降低误差和效率指数，以确定我们框架的鲁棒性和效率。
In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier-Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.
