基于smolyak稀疏网格与POD的非侵入式降维模型及其多相流应用

In various numerical simulations, many runs (e.g.,hundreds or thousands) of model are needed in the context of uncertainty studies, parameters sensitivity analysis or optimal design. However, high computational cost of non-reduced full model renders those studies or analysis very difficult. In this cases, model reduction technology has shown to be a viable way of mitigating the expensive CPU computational cost of full order model. In this project, a new non-intrusive reduced order model based on Smolyak sparse grid and proper orthogonal decomposition(POD) will be presented. This method constructs a set of super-cube interpolation functions for POD coefficients. The novelty of this method resides in that it solves reduced system without projecting governing equations onto the reduced space, it uses the Smolyak sparse grid collocation method to calculate the POD coefficients..This method has a potential to achieve a factor of 200-1500 times speed-up of CPU cost while keeping over 99% accuracy, therefore, some problems need many runs of model will become practical.

在各种数值模拟中，经常要运行数值计算模型成千上万次以便进行如模型不确定性分析，参数敏感性分析和优化等。原模型的运行时间过长导致这些问题变得异常困难。降维模型为解决此类问题提供了途径。本课题提出了基于Smolyak稀疏网格和POD的非侵入式降维模型。此模型对POD系数构造了一组超高维插值函数。本课题的特色在于解降维模型的方式为通过插值函数获取，而非传统的将原有模型投影到降维空间后进行解方程获取。此方法有望将模型的运行速度根据问题的复杂程度提高200-1500倍，但同时可保证99%以上的精确度，从而使各种复杂的需要反复运行模型的工程应用成为现实。

项目在计算力学基础算法领域，针对计算效率低这一核心科学问题取得突破性进展，为新一代突发应急计算理论奠定坚实的理论基础， 保障国家人民生命财产安全，以及保障国家安全。 特别在复杂计算模型的快速计算方法；超高维数据的稀疏表达；机理与数据的混合建模以及计算模型的非线性降维方面有突出贡献。此课题研究的算法让计算时间过长的流体、流固耦合、空气污染、多相流等问题计算效率提高100-10000 倍，且保证了计算的稳定和精度。这使得要运行模型成千上万次的应用如参数敏感性分析、不确定性分析、数据同化等应用成为可能。并且为海洋，洪山，滑坡等自然灾害的实时预警和决策提供了坚实的基础。