Solving Laplace’s Equation by Cell-Centered Finite Volume Method on Unstructured Grids

• Main Authors: Jui-Chi Hung, 洪瑞祺
• Other Authors: Yih-Jena Jan
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/54845486365317191748

碩士 === 國立高雄海洋科技大學 === 輪機工程研究所 === 97 === In this study a cell-centered finite volume method on unstructured grids is used to solve Laplace’s equation. The two- dimensional and three-dimensional heat conduction problems in steady and unsteady states are analyzed. First, Laplace’s equation is discretized to obtain differential equations with first-order and hyper-order accuracy. Then, the converged solution is determined within specific iterative times using the conjugate gradient iterative method (P-CG). This study compares the calculated results of first-order accuracy with those of hyper-order accuracy in steady and unsteady states. The experiment indicates that the results of first-order accuracy are consistent with those of hyper-order accuracy on unstructured grids in steady state. Moreover, applying the cell-centered finite volume method on problems in unsteady state will reduce the number of iterative times, and converges much faster.