论文标题
BDF2--氨齿牛顿算法，用于宾厄姆流的数值解决方案，带有温度依赖参数
A BDF2-Semismooth Newton Algorithm for the Numerical Solution of the Bingham Flow with Temperature Dependent Parameters
论文作者
论文摘要
本文通过半齿牛顿方法，专门用于与温度相关参数的非等热宾汉流量的数值解。我们讨论有关此问题的主要理论方面。主要是，我们专注于解决方案和乘数公式的存在，这使我们建立了涉及Navier-Stokes类型方程和抛物线能量PDE的PDE耦合系统。此外，我们为这种偏微分方程的耦合系统提出了一个Huber正则化，并简要讨论了这些正规化问题的良好姿势。基于所谓的（交叉格里德$ \ mathbb {p} _1 $）的详细有限元离散化 - $ \ mathbb {q} _0 $元素是针对空间变量的，涉及加权刚度和质量矩阵。空间离散后，将二阶BDF方法用作时间前进的技术，每次迭代中引导到非平滑方程系统，该方程式适合通过半齿的牛顿算法来解决。因此，我们提出并讨论了SSN算法的主要特性，包括收敛属性。本文通过两个计算实验结束，这些计算实验表现出数值方法的主要特性。
This paper is devoted to the numerical solution of the non-isothermal instationary Bingham flow with temperature dependent parameters by semismooth Newton methods. We discuss the main theoretical aspects regarding this problem. Mainly, we focus on existence of solutions and a multiplier formulation which leads us to a coupled system of PDEs involving a Navier-Stokes type equation and a parabolic energy PDE. Further, we propose a Huber regularization for this coupled system of partial differential equations, and we briefly discuss the well posedness of these regularized problems. A detailed finite element discretization, based on the so called (cross-grid $\mathbb{P}_1$) - $\mathbb{Q}_0$ elements, is proposed for the space variable, involving weighted stiffness and mass matrices. After discretization in space, a second order BDF method is used as a time advancing technique, leading, in each time iteration, to a nonsmooth system of equations, which is suitable to be solved by a semismooth Newton algorithm. Therefore, we propose and discuss the main properties of a SSN algorithm, including the convergence properties. The paper finishes with two computational experiment that exhibit the main properties of the numerical approach.
