连铸中的自由边界问题的边界元解法
Solving the Free Boundary Problem in Continuous Casing by Using Boundary Element Method
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摘要: 本文应用边界元法求解钢铁生产中连铸工艺出现的自由边界问题。首先,对较一般的连铸过程的数学模型进行简化并给出相应的边界积分方程,以及叙述了用边界元法求解该问题的步骤。然后,我们给出了一个计算实例,并对该方法的收敛快慢、对初值的敏感性和对区域形状的适应性等问题进行了探讨。最后,针对一种简化的模型,将数值解与解析解进行比较,两者吻合较好。Abstract: In this paper.the authors solve the free boundary problem(FBP) in continuous casiing by using boundary element method(BEM).First,we simplify the general mathematical model for continuous casting to a practicable model,and give the boundary integral equations with partial unknown boundary for this model,and describe in detail the steps of calculating this FBP by using the BEM.Next,wepresent the result of our numerical experiments,and discuss the stability,convergence and applicaiion of our method.At last.we simplify the former model so that it has ananalytic solution.and we compare its numerical solution resulted from our method withits analytic solution.
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Key words:
- continuous casting /
- free boundary problem /
- boundary element method /
- numencal solution
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[1] 张振忠、徐平、蒋运采、林尤栋.水平连铸控制系统的现状及其发展趋势.铸造设备研究.14(1)(1992).27-30, [2] 吴兴宝.钢铁生产中的自由边界问题.应用数学.1(1.2)(1988).133-143 [3] J.Crank,Free and Moving Boundary Problems,Clavendon Press,Oxford(1984). [4] 大中逸雄.《计算机传热凝固解析入门:铸造}i程中韵应用》.许云祥译.机械工业出版社.北京(1988). [5] C.A.Brebbia,et al.,Boundary Element Techniques:Theory and Application in Engineering,Springer-Verlag,Berlin(1984).
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