Journal of Changjiang River Scientific Research Institute ›› 2025, Vol. 42 ›› Issue (4): 211-218.DOI: 10.11988/ckyyb.202401142
• Numerical Manifold Method Based on Independent Covers • Previous Articles
					
													SU  Hai-dong1,2(
), SONG  Wen-shuo1, GONG  Ya-qi1,2, HAN  Lu-chao1, WEI  Yu-xia1
												  
						
						
						
					
				
Received:2024-02-02
															
							
																	Revised:2024-05-07
															
							
															
							
																	Published:2025-04-01
															
							
																	Online:2025-04-01
															
						CLC Number:
SU Hai-dong, SONG Wen-shuo, GONG Ya-qi, HAN Lu-chao, WEI Yu-xia. General Formulas and Program Design for Manifold Method Based on Independent Covers Ⅲ: Example Verification[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 211-218.
																													Fig.1 Comparison between numerical solutions and theoretical solutions of one-dimensional steady state analysis examples (10 covers and 10-order polynomials)[1]
																													Fig.2 Comparison between numerical solutions and theoretical solutions of one-dimensional steady state analysis examples (60 covers and 3-order polynomials)[1]
| t/s | u值 | |
|---|---|---|
| 数值解 | 理论解 | |
| 0.1 | 0.151 059×100 | 0.151 059×100 | 
| 0.2 | 0.562 983×10-1 | 0.562 986×10-1 | 
| 0.3 | 0.209 827×10-1 | 0.209 829×10-1 | 
| 0.4 | 0.782 035×10-2 | 0.782 049×10-2 | 
| 0.5 | 0.291 469×10-2 | 0.291 475×10-2 | 
| 0.6 | 0.108 632×10-2 | 0.108 635×10-2 | 
| 0.7 | 0.404 883×10-3 | 0.404 892×10-3 | 
| 0.8 | 0.150 906×10-3 | 0.150 906×10-3 | 
| 0.9 | 0.562 467×10-4 | 0.562 440×10-4 | 
| 1.0 | 0.209 655×10-4 | 0.209 625×10-4 | 
Table 1 Comparison of u values at different instances when x=0.5
| t/s | u值 | |
|---|---|---|
| 数值解 | 理论解 | |
| 0.1 | 0.151 059×100 | 0.151 059×100 | 
| 0.2 | 0.562 983×10-1 | 0.562 986×10-1 | 
| 0.3 | 0.209 827×10-1 | 0.209 829×10-1 | 
| 0.4 | 0.782 035×10-2 | 0.782 049×10-2 | 
| 0.5 | 0.291 469×10-2 | 0.291 475×10-2 | 
| 0.6 | 0.108 632×10-2 | 0.108 635×10-2 | 
| 0.7 | 0.404 883×10-3 | 0.404 892×10-3 | 
| 0.8 | 0.150 906×10-3 | 0.150 906×10-3 | 
| 0.9 | 0.562 467×10-4 | 0.562 440×10-4 | 
| 1.0 | 0.209 655×10-4 | 0.209 625×10-4 | 
| [1] | SU Hai-dong. General Formulas and Program Design for Manifold Method Based on Independent Covers Ⅰ:General Formulas [J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 193-201. | 
| [2] | SU Hai-dong, YANG Zhen, XIE Zhi-qiang, QI Yong-feng, GONG Ya-qi. General Formulas and Program Design for Manifold Method Based on Independent Covers Ⅱ: General Program Design [J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 202-210. | 
| [3] | JIA Zhen, YANG Dong-mei, ZHENG Hong. A New Method to Deal with Weak Discontinuous Interface in Seepage Analysis Based on Numerical Manifold Method [J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(12): 133-137. | 
| [4] | WANG Fang-yi, ZHENG Hong. Numerical Manifold Method for Unbounded Domain Problems [J]. Journal of Changjiang River Scientific Research Institute, 2023, 40(7): 110-117. | 
| [5] | SU Hai-dong, HAN Lu-chao, XIE Zhi-qiang. Analysis of Thin Curved Beam and Curved Shell with Exact Geometry Using Piecewise-defined Series Solutions [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 144-151. | 
| [6] | SU Hai-dong, WEI Yu-xia, HAN Lu-chao, XIE Zhi-qiang. Rigid Connection Between Plate Shell Elements and Solid Elements in the Manifold Method Based on Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 152-158. | 
| [7] | SU Hai-dong, DONG Peng, XIE Zhi-qiang. Solving Geometric Nonlinear Problems in Fixed Meshes of Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(9): 159-166. | 
| [8] | YANG Shi-kou, AI Hua-dong. Essential Boundary Treatment of Three-dimensional Numerical Manifold Method [J]. Journal of Changjiang River Scientific Research Institute, 2022, 39(3): 137-142. | 
| [9] | SU Hai-dong, FU Zhi, XIE Zhi-qiang. Automatic Two-dimensional Computation Based on Arbitrary Mesh Division [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(7): 160-166. | 
| [10] | SU Hai-dong, FU Zhi, XIE Zhi-qiang. Numerical Computations Based on Cover Meshes with Arbitrary Shapes and on Exact Geometric Boundaries [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(7): 167-174. | 
| [11] | LIU Ya-jun, GONG Ya-qi, SU Hai-dong. Numerical Method for Solving One-dimensional Convection-Diffusion Equation Based on Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(7): 175-182. | 
| [12] | ZHANG You-liang, MO Si-yang. Parallel Algorithm of Cover System Generation in Numerical Manifold Method [J]. Journal of Changjiang River Scientific Research Institute, 2020, 37(10): 1-8. | 
| [13] | SU Hai-dong. Application Prospect of Manifold Method Based on Independent Covers in Hydraulic Structure Analysis [J]. Journal of Changjiang River Scientific Research Institute, 2019, 36(6): 1-8. | 
| [14] | GAO Dai-heng, GUO Hong-wei, ZHENG Hong. A Rigorous Mass Lumping Scheme for Vibration of Beams [J]. Journal of Changjiang River Scientific Research Institute, 2019, 36(4): 118-122,139. | 
| [15] | SU Hai-dong, ZHOU Chao, XIE Zhi-qiang, CHEN Qin. Analysis of Curved Shells with Exact Geometric Description Using Numerical Manifold Method Based on Independent Covers [J]. Journal of Changjiang River Scientific Research Institute, 2018, 35(4): 158-166. | 
| Viewed | ||||||
| 
										Full text | 
									
										 | 
								|||||
| 
										Abstract | 
									
										 | 
								|||||