自适应步长顺序耦合法及其在瞬态场耦合问题分析中的应用

Self-adaptive step sequential-interaction method and its application in transient-fields coupling problems

采用顺序耦合分析方法求解瞬态场耦合问题,在各迭代步累积的非平衡载荷残差会危及数值积分收敛性,选取极小迭代步长能够保证求解的精度及稳定性,但求解效率低。通过提取迭代节点耦合状态变量数值解,构造基于拉格朗日基函数的一阶变步长三点数值微分公式,建立步长自适应调整策略,在求解该类问题时根据耦合状态变量数值曲线波动性动态调整迭代步长。对于包含多个耦合状态变量的复杂瞬态场耦合问题,通过在迭代节点比对各变量独立步长与系统步长取值,建立多状态变量问题数据交互及步长自适应调整机制。构建异构计算机辅助工程系统联合仿真平台,对低压塑壳断路器短路分断中的运动场与电磁场耦合问题进行分析,结果表明该方法能有效求解此类问题,且求解效率较传统固定步长方法有明显提高。

Non-equilibrium load residual accumulated in each iterative step could endangered numerical integration convergence when solving transient-fields coupling problems.Keeping the step small enough could guarantee the solution stability and precision but the efficiency was low.By extracting variable numerical solution of iterative step node coupling,a self-adaptive step sequential-interaction strategy was proposed,which could dynamically adjust the iteration steps according to the curve slope of coupling variables and a three-point derivation formula based on interpolation polynomial of Lagrange was constructed.For transient-fields coupling which included more than one coupling variables,a multimode variable problem of data interaction and self-adaptive step adjusting mechanisms were established by comparing the value of independent steps and system step.The unified simulation platform for heterogeneous Computer Aided Engineering（CAE） system was set up.Coupling problem of electromagnetic field and motion field which brought by interruption of low voltage moulded case circuit breaker was analysed.The result showed that the method was effective.Comparing to the method with fixed step,the solution efficiency was remarkably improved.