A simple locally conservative Galerkin (LCG) finite-element method for transient conservation equations

Nithiarasu P

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A simple locally conservative Galerkin (LCG) finite-element method for transient conservation equations

机译：暂态守恒方程的简单局部保守Galerkin（LCG）有限元方法

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In this article a locally conservative Galerkin finite-element approach is proposed for transient conservation equations using linear triangular elements. The method proposed follows a simple postprocessing procedure at each time step and evaluates a numerical flux on the element edges. The proposed method requires inversion of only a 3 x 3 matrix, per element, in its implicit form. The system of simultaneous equations is solved over individual elements independently of the surrounding element equation sets. The situation of multiple solutions at a node is eliminated by taking the average among the solutions obtained from the surrounding elements. Both diffusion and convection-diffusion problems are solved in one and two dimensions and compared with analytical solutions.

机译：在本文中，针对使用线性三角元素的瞬态守恒方程，提出了局部保守的Galerkin有限元方法。所提出的方法在每个时间步均遵循简单的后处理程序，并评估元素边缘的数值通量。所提出的方法要求每个元素以其隐式形式仅反转3 x 3矩阵。联立方程组可以独立于周围元素方程组而对单个元素进行求解。通过取从周围元素获得的解的平均值，可以消除节点上多个解的情况。一维和二维问题都可以解决扩散和对流扩散问题，并与解析解进行比较。

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《Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology》 |2004年第4期|共14页
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Nithiarasu P;
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正文语种 eng
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1. A simple locally conservative Galerkin (LCG) finite-element method for transient conservation equations [J] . Nithiarasu P Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology . 2004,第4期

机译：暂态守恒方程的简单局部保守Galerkin（LCG）有限元方法
2. Application of a locally conservative Galerkin (LCG) method for modelling blood flow through a patient-specific carotid bifurcation [J] . R. L. T. Bevan, P. Nithiarasu, R. Van Loon, International Journal for Numerical Methods in Fluids . 2010,第10a12期

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3. An element-wise, locally conservative Galerkin (LCG) method for solving diffusion and convection-diffusion problems [J] . Thomas CG, Nithiarasu P International Journal for Numerical Methods in Engineering . 2008,第5期

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4. A locally conservative Eulerian-Lagrangian control volume method for transient advection-diffusion equations [C] . Hong Wang, Mohamed Al-Lawatia XIVth International Conference on Computational Methods in Water Resources (CMWR XIV), Jun 23-28, 2002, Delft, The Netherlands . 2002

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A simple locally conservative Galerkin (LCG) finite-element method for transient conservation equations

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