A non-intrusive reduced basis approach for parametrized heat transfer problems

Abstract

Computation Fluid Dynamics (CFD) simulation has become a routine design tool for i) predicting accurately the thermal performances of electronics set ups and devices such as cooling system and ii) optimizing configurations. Although CFD simulations using discretization methods such as finite volume or finite element can be performed at different scales, from component/board levels to larger system, these classical discretization techniques can prove to be too costly and time consuming, especially in the case of optimization purposes where similar systems, with different design parameters have to be solved sequentially. The design parameters can be of geometric nature or related to the boundary conditions. This motivates our interest on model reduction and particularly on reduced basis methods. As is well documented in the literature, the offline/online implementation of the standard RB method (a Galerkin approach within the reduced basis space) requires to modify the original CFD calculation code, which for a commercial one may be problematic even impossible. For this reason, we have proposed in a previous paper, with an application to a simple scalar convection diffusion problem, an alternative non-intrusive reduced basis approach (NIRB) based on a two-grid finite element discretization. Here also the process is two stages: offline, the construction of the reduced basis is performed on a fine mesh; online a new configuration is simulated using a coarse mesh. While such a coarse solution, can be computed quickly enough to be used in a rapid decision process, it is generally not accurate enough for practical use. In order to retrieve accuracy, we first project every such coarse solution into the reduced space, and then further improve them via a rectification technique. The purpose of this paper is to generalize the approach to a CFD configuration.

A Non-Intrusive Reduced Basis Method for Urban Flows Simulation

“…In practice, how can we construct the rectification matrix R ? The construction process, described in [8], starts with the computation of the following matrix…”

“…Besides, the intrusive nature of RB methods can be problematic when one does not have access to the simulation code that solves the physical model (industrial codes for example). For these two main reasons, the Non-Intrusive Reduced Basis (NIRB) method [7,8,9] is a good alternative to RB methods in urban CFD applications. We propose in this work to apply the NIRB method to a 2D CFD simulation of the airflow along a backward-facing step, which represents the air recirculation that occurs behind a building.…”

Error estimate of the non-intrusive reduced basis method with finite volume schemes

“…Several papers have underlined the efficiency of the NIRB method in the finite element context, illustrated both with numerical results presenting error plots and the online part computational time [8][9][10]25]. However, to the best of our knowledge, works with Finite Volume (FV) schemes have not yet been studied with a nonintrusive approach [7,21,23,28,29], and they are often preferred to finite element methods in an industrial context.…”

“…We introduce ℎ ( ) = ∫︀ Ω Π ℎ ℎ ( ) • Π ℎ Φ ℎ dx. The rectification process, explained in [8,10,25], can be employed in addition of the NIRB classical algorithm. This implies that if the true solution is in the reduced space, then the NIRB method will give this true solution.…”

Constrained multi-fidelity surrogate framework using Bayesian optimization with non-intrusive reduced-order basis

“…The present work aims at predicting the system response based on a limited number of prior HF evaluations and the LF vector responses. To this end, the Non-Intrusive Reduced Basis (NIRB) [11] methodology is extended to a multi-fidelity optimization context called Multi-Fidelity Non-Intrusive Reduced Basis (MFNIRB) with a correction method within the Bayesian optimization framework.…”