Authors:
J. Du a,b, F. Fang b, C.C. Pain b, I.M. Navon c,？ , J. Zhu a, D.A. Ham b,d
a Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
b Applied Modeling and Computation Group, Department of Earth Science and Engineering, Imperial College, Prince Consort Road, London SW7 2BP, UK
c Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA
d Grantham Institute for Climate Change, Imperial College, Prince Consort Road, London SW7 2BP, UK
Abstract：
A new scheme for implementing a reduced order model for complex mesh-based numerical models (e.g. finite element unstructured mesh models), is presented. The matrix and source term vector of the full model are projected onto the reduced bases. The proper orthogonal decomposition (POD) is used to form the reduced bases. The reduced order modeling code is simple to implement even with complex governing equations, discretization methods and nonlinear parameterizations. Importantly, the model order reduction code is independent of the implementation details of the full model code. For nonlinear problems, a perturbation approach is used to help accelerate the matrix equation assembly process based on the assumption that the discretized system of equations has a polynomial representation and can thus be created by a summation of pre-formed matrices. In this paper, by applying the new approach, the POD reduced order model is implemented on an unstructured mesh finite element fluid flow model, and is applied to 3D flows. The error between the full order finite element solution and the reduced order model POD solution is estimated. The feasibility and accuracy of the reduced order model applied to 3D fluid flows are demonstrated.
Key words：
POD reduced order model, 3D flows, Finite element, Unstructured mesh, Numerical simulation
Citation:
J. Du et al. POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. Computers and Mathematics with Applications 65 (2013) 362–379