复杂流动与传热问题的高效POD低阶模型研究

数值计算是解决实际生产运行难题、研究复杂流动与传热机理的有效手段，但往往需要很大计算量。特征正交分解(POD)低阶模型能以较小的代价显著降低计算负荷，有望解决"海量"计算问题。然而POD在复杂流动与传热领域的应用尚需解决一系列难题，包括研究复杂几何区域和复杂组分流体的POD建模方式、评价不同POD低阶模型的综合性能和适用范围等。本项目针对复杂流动与传热POD建模中存在的上述问题开展研究，建立复杂几何区域内非结构化网格和贴体坐标下的POD低阶模型和复杂组分流体的多组分多相非线性耦合POD低阶模型，比较不同POD投影和插值低阶模型的计算精度、速度和健壮性，提出或确定各自的适用范围与条件。通过以上研究，完善POD低阶模型理论和方法，并促进其在复杂流动与传热领域内的应用。

Numerical simulation is an effective manner to solve real problems and study mechanisms of complex flow and heat transfer, but it usually needs huge computations. Reduced-order modeling by the proper orthogonal decomposition (POD) can reduce the computational burden with relatively small cost and has potential to solve the huge computational problems. However, applications of POD in the field of complex flow and heat transfer are restricted to a series of problems, including POD modeling for complex geometrical regions and complex compositional fluids, overall evaluation of different POD models and so on. Therefore, this project will focus on these problems in complex flow and heat transfer, establish POD reduced-order models for unstructured grids and adaptive coordinates on complex geometries and multi-variable-nonlinear coupling of complex fluids, and distinguish the effective scopes and conditions of different POD projection and interpolation models by comparing their accuracies, speeds and robustness. Through the above researches, it is expected to modify the theories and methods of POD reduced-order modeling and promote their applications in complex flow and heat transfer.