变密度宾汉流数值求解的间断伽辽金与半光滑牛顿方法
A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density
AI总结：
本文针对变密度宾汉流问题，提出基于Huber光滑化的局部双黏度正则化方法，结合二阶散度协调离散与间断伽辽金格式，并采用半光滑牛顿法求解全离散系统，通过数值算例验证了方法的有效性。
摘要：
本文致力于研究变密度宾汉流。我们基于Huber光滑化步骤提出了应力张量的局部双黏度正则化方法。随后，我们的计算方法基于对Huber正则化宾汉本构方程的二阶散度协调离散，并结合质量密度的间断伽辽金格式。我们利用散度协调和间断伽辽金公式的性质引入迎风离散以稳定该格式。分析了连续问题和全离散格式的稳定性。此外，提出了一种半光滑牛顿方法，用于在每个时间步求解所得到的全离散方程组。最后，给出了若干数值算例，以说明该问题的主要特征和数值格式的性质。
英文摘要：
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.
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