参数化高保真模型的快速求解方法

Fast solution methods of parameterized high-fidelity models

基于求解偏微分方程的高保真数值模拟已成为核能创新研究的重要手段.然而,即使借助超级计算机,经典的高分辨率数值方法在处理需要多次求解或需要快速甚至实时求解的问题时仍然面临效率的挑战,模型降阶是求解这类问题的有效手段.针对参数化热-力耦合和参数化流动这两类核工程的基本问题,本文分别归纳和推导了利用缩减基有限元方法和本征正交分解-伽辽金投影方法求解耦合问题和非线性问题的原理和步骤,并通过T型管接头的热应力分布和后台阶流动两个典型算例对建立的降阶模型进行了验证.结果表明,在保证精度的前提下,在线阶段降阶模型的计算效率提升了3–5个数量级.高精度、高效率的模型降阶方法将是数值反应堆技术走向工程应用的重要技术手段.

High-fidelity simulation based on solving partial differential equations has become an indispensable approach in innovative research of nuclear energy. However, due to the prohibitively high computation cost, it is yet unfeasible to run simulations on the whole reactor core level with all the physics resolved on fine meshes, especially in the analysis which need carry out many times of calculations. Model order reduction strategies are promising ways to achieve significant speedups by replacing the original large-scale model by a reduced order model of substantially smaller scale. Two effective model order reduction techniques, i.e., the reduced basis finite element method and the POD-Galerkin method,are studied and applied in the present study to solve the transient thermo-elastic problem and the fluid dynamics problem,respectively. For the former, the boundary conditions, the physical parameters and the body heat source are treated as parameters. The greedy-POD algorithm is applied to construct reduced basis space and the for the latter, the Reynolds number is treated as a parameter. The pure POD method is applied to construct the basis space. During on the online stage, three to five orders of computation speed up has been achieved by using the built reduced order models compared with that by the full order models while the accuracy of the results is well ensured. It is demonstrated that model order reduction techniques will be a practical way to deploy numerical reactors.