大体积混凝土稳定温度场的蒙特卡罗解

Monte Carlo Method of Steady Thermal Field in Mass Concrete

利用一种求偏微分方程的新方法———蒙特卡罗算法通过不规则网格随机游动来求解大体积混凝土稳定温度场。应用这种方法可以在不分解总刚矩阵的情况下,求解各单个结点上的温度值,并可以通过随机抽样次数来控制精度。文中给出了相应的随机游动模型,并通过实例计算加以验证。计算表明,蒙特卡罗法的结果同其它方法结果吻合很好,新方法是可行的。

In this paper, the problem of mass concrete steady thermal field was solved by using Monte Carlo method with irregular grid random walk. By using this method, temperature value on any single node could be solved,without forming the total stiffness matrix, and the preeisio could be easily controlled according to the times of Random Walks. The appropriate random walks model was offered and the method could be tested and verified with living example. The final calculation demonstrated that the result obtained by Monte Carlo method agreed well with that obtained by the other ones.