Abstract An adaptive algorithm was developed to handle some multiphase situations where outlet information is included in results or multiple inlets/outlets are implemented while only flow rates through inlets/outlets are known. This algorithm includes a first-order expanded Bernoulli equation and a mixed approximation algorithm. The expanded Bernoulli equation offers an initialization value for a concerned object for subsequent approximation processes. The mixed approximation algorithm completes final convergence via iteration and correction. The executed code was successfully compiled into a commercial computational fluid dynamics software. To test the algorithm, a series of corresponding experiments were performed. Three key parameters including the validity of the initialization condition from the expanded equation, convergence efficiency and reliability were evaluated and discussed. The results show that this boundary condition could accomplish the desired functions and maintain errors lower than 15% compared to experimental data, and in less rigorous applications, the error may be approximate to 5%.

中文翻译：

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欧拉-欧拉多相数值模拟的多出口自适应边界条件

摘要 开发了一种自适应算法来处理一些多相情况，其中出口信息包含在结果中或实施多个入口/出口而只有通过入口/出口的流速是已知的。该算法包括一阶扩展伯努利方程和混合逼近算法。扩展的伯努利方程为后续近似过程提供了相关对象的初始化值。混合逼近算法通过迭代和修正完成最终收敛。执行的代码被成功编译成商业计算流体动力学软件。为了测试算法，进行了一系列相应的实验。三个关键参数，包括扩展方程初始化条件的有效性，对收敛效率和可靠性进行了评估和讨论。结果表明，与实验数据相比，该边界条件可以完成所需的功能并保持误差低于 15%，在不太严格的应用中，误差可能接近 5%。