曲线交错网格拉格朗日流体力学的一种延迟校正连续伽辽金方法
A Deferred Correction, Continuous Galerkin Method for Curvilinear Staggered-Grid Lagrangian Hydrodynamics
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中文总结 AI 辅助
本文提出一种连续伽辽金延迟校正（cG-DeC）方法求解拉格朗日流体力学方程，结合高阶有限元与显式时间积分，避免全局矩阵求逆，并改进超黏性模型以稳定强激波，数值实验验证了精度与鲁棒性。
中文摘要 AI 辅助
我们提出了一种用于拉格朗日流体力学方程的连续伽辽金延迟校正（cG-DeC）方法。该方案将高阶连续有限元离散与显式延迟校正时间积分器相结合，形成了一种在每个更新步骤中无需反转全局稀疏质量矩阵的格式。为了在强激波存在下稳定该方法，我们引入了超黏性模型的一种修改，该修改与cG-DeC框架兼容，并且同样不需要全局求解来构造多调和算子的有限元近似。我们进一步提出了DeC迭代的一种替代重构，该重构具有简单的递归算法结构，并提供了对显式DeC应用于双曲偏微分方程时先前观察到的收敛行为的深入理解。分析了所得全离散格式的动量守恒和总能量守恒。一系列数值实验展示了cG-DeC方案的精度和鲁棒性。并与连续伽辽金龙格-库塔（cG-RK）方法进行了比较。
英文摘要
We present a continuous Galerkin, Deferred Correction (cG-DeC) method for the equations of Lagrangian hydrodynamics. The proposed scheme combines a high-order continuous finite element discretization with an explicit Deferred Correction time integrator, yielding a formulation that avoids the inversion of a global sparse mass matrix at each update. To stabilize the method in the presence of strong shocks we introduce a modification of the hyperviscosity model that is compatible with the cG-DeC framework and likewise does not require a global solve to construct the finite element approximation to the polyharmonic operator. We further present an alternative reformulation of the DeC iteration which admits a simple recursive algorithmic structure and provides insight into previously observed convergence behavior of explicit DeC applied to hyperbolic partial differential equations. Conservation of momentum and total energy of the resulting fully discrete scheme is analyzed. A set of numerical experiments illustrates the accuracy and robustness of the cG-DeC scheme. Comparisons with a continuous Galerkin Runge-Kutta (cG-RK) method are provided.
发表机构
- Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
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