Reduced Basis Methods and A Posteriori Error Estimators for Heat Transfer Problems
This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — material properties, boundary conditions and sources, and geometry — we would like to compute certain outputs of engineering interest — heat fluxes and average temperatures. The certified reduced basis method provides both (i) a very inexpensive yet accurate output prediction, and (ii) a rigorous bound for the error in the reduced basis prediction relative to an underlying expensive high-fidelity finite element discretization. The feasibility and efficiency of the method is demonstrated for three natural convection model problems: a scalar steady forced convection problem in a rectangular channel is characterized by two parameters — Peclet number and the aspect ratio of the channel — and an output –- the average temperature over the domain; a steady natural convection problem in a laterally heated cavity is characterized by three parameters — Grashof and Prandtl numbers, and the aspect ratio of the cavity — and an output — the inverse of the Nusselt number; and an unsteady natural convection problem in a laterally heated cavity is characterized by two parameters — Grashof and Prandtl numbers— and a timedependent output — the average of the horizontal velocity over a specified area of the cavity.
- View record in Web of Science
Keywords: Reduced basis method ; error estimators ; steady and unsteady heat transfer ; natural and forced convection ; parametrized systems ; Graetz flow ; Peclet number ; Grashof number ; Prandtl number
presented in the Computational Section of the conference. EPFL-IACS report 05.2009, peer reviewed.
Record created on 2009-05-20, modified on 2016-08-08