从数值解浅析热传导方程的精确解 - 南京师范大学学报（工程技术版）.PDF

7 3 () V o.l 7 No. 3 2007 9 JOU RNAL O F NAN JING NO RM AL UN IVERS ITY ( ENG INEER ING AN D TECHNO LOGY ED IT ION ) Sep, 2007 从数值解浅析热传导方程的精确解 1 2 2 黄庆宏, 张 敏, 许 彬 ( 1. , 2 10042; 2. , 2 10094) [] . , . , , 3, , . [] , , [ ] TK 124 [ ] A [] 2007) AnalyzingExact Solutions ofHeat Conduction Equations by ComparingW ithNumerical Solutions 1 2 2 H uang Q inghong , Z hang M in , X u B in ( 1. School of P ow er Eng n eer ng, N anj ng N orma lU n vers ty, N anj ng 2 10042, Ch na; 2. Col lege of Pow er Eng n eer ng, N anj ng U n vers ty of Sc ence and T echnology, N anj ng 2 10094, Ch na) Abstract: It s an mportant me thod tha t the exact so lut ons of the heat conduct on equat ons test the correctness o f the num er ca l so lut ons. M eanw h le, the sam e m po rtant s to u se the nume r cal so lut ons ana ly z ng the exact so lu t ons for perfect resu lts. The hea t conduct on equa t on w as so lved u s ng based ce ll fn te vo lum e m ethod and the secondary order upw nd schem e n structured m esh. Three examp les are g ven show ng up the def c ency o f the exact solut on o f the class ca l heat conduct on equat on n the paper. A nd, the nte rnal relat on and the com plem entar t es be wt een the exac t and the num er cal so lut ons are d scussed. K ey ords: num er cal so lut ons, exact so lut ons, heat conduct on equat on 1 基本导热方程 , . , , . , : 1