二维潜水运动方程的分裂解法
Splitting Method for Two-Dimensional Phreatic Flow Equation
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摘要: 本文通过对二维潜水运动方程的变形,按其在形式上所代表的意义不同,用和分裂方法,把它分解成“对流”和“扩散”两部分。对前者,用交替方向有限差分法求解;对后者,用交替方向Picard迭代法进行计算,从而达到获得整个问题的解的目的。最后,用数值例子验证了所提方法的有效性,并与线性化的有限差分法作了对比,证明本文所提方法在计算精度上有所提高。Abstract: In this paper, according to their difference in "physical meaning", twodimensional phreatic flow equation, which has been transformed, is devided into two parts──advection and dispersion by the splitting method. For the former, alternating direction finite difference method will be used and for the faller, it is resolved by altemating direction Picarditeration, therefore, the aim of computing the solution of whole problem will be reached. At last, the validitt of the algorithms is proved by the numerical example. The comparison of the proposed method with the conventional finite difference (linearized) is made. The results show that the precision of calculationby the method proposed in this paper is better than the conyentional methods.
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Key words:
- phreatic flow equation /
- nonlinear /
- splitting method /
- finite difference method /
- Picard iteration
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[1] 王新民等,《应用数值方法》,吉林教育出版社(1992) [2] 孙讷正,《地下水流灼数学模型和数值方法》,地质出版社(1981) [3] 吴江航等,《计算流体动力学的理论、方法及应用》,科学出版社(1988)
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