论文标题
不连续的galerkin和半齿牛顿方法，用于宾汉流量的数值解决方案，其密度可变
A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density
论文作者
论文摘要
本文致力于研究宾厄姆流量的研究。我们根据Huber平滑步骤提出应力张量的局部双粘度正则化。接下来，我们的计算方法基于Huber正规化Bingham组成型方程的二阶，差异 - 符合差异的离散化，并与不连续的Galerkin方案结合使用，用于质量密度。我们利用差异构象和不连续的Galerkin公式的特性来纳入前风离散以稳定配方。分析了连续问题的稳定性和全差异方案。此外，提出了一种半齿牛顿方法，用于在每个时间步骤求解获得的方程式系统。最后，介绍了一些数字示例，这些示例说明了问题的主要特征和数值方案的属性。
This paper is devoted to the study of Bingham flow with variable density. We propose a local bi-viscosity regularization of the stress tensor based on a Huber smoothing step. Next, our computational approach is based on a second-order, divergence-conforming discretization of the Huber regularized Bingham constitutive equations, coupled with a discontinuous Galerkin scheme for the mass density. We take advantage of the properties of the divergence conforming and discontinuous Galerkin formulations to incorporate upwind discretizations to stabilize the formulation. The stability of the continuous problem and the full-discrete scheme are analyzed. Further, a semismooth Newton method is proposed for solving the obtained fully-discretized system of equations at each time step. Finally, several numerical examples that illustrate the main features of the problem and the properties of the numerical scheme are presented.
