A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems

作者：Luo, Zhendong^*; Li, Hong; Sun, Ping; An, Jing; Navon, Ionel Michael

来源：Mathematics and Computers in Simulation, 2013, 89: 50-68.

DOI：10.1016/j.matcom.2012.11.012

• Proper orthogonal decomposition
• Finite volume element formulation
• Error estimate
• Two-dimensional solute transport problems
• Numerical simulation

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional solute transport problems, which have real life practical applications. We then provide error estimates between the reduced-order POD FVE solutions and classical FVE solutions and we provide implementation of an extrapolation algorithm for solving the reduced-order FVE formulation. Thus, we provide the theoretical basis for practical applications. A numerical example is then used to ascertain that the results of numerical computation are consistent with the theoretical derivations. Moreover, it is shown that the reduced-order FVE formulation based on POD method is both feasible and efficient for solving two-dimensional solute transport problems.

• 出版日期2013-3
• 单位华北电力大学（保定）; 内蒙古大学; 贵州师范大学; 华北电力大学