Nonintrusive reduced‐order modeling approach for parametrized unsteady flow and heat transfer problems

Abstract

A novel nonintrusive reduced-order modeling approach is proposed for parametrized unsteady flow and heat transfer problems. A set of reduced basis functions are extracted via a proper orthogonal decomposition (POD) method from a collection of high-fidelity numerical solutions (snapshots of spatial distribution at a series of time steps) that are computed for properly chosen parameters (e.g., material property, initial/boundary conditions) using a full-order model (finite-volume/finite-element methods). Here, the time dimension is treated separately from other parameters, reflecting the dynamic features of the flow problems. Dynamic mode decomposition is used to decompose the time-resolved data (POD coefficients) into dynamics modes and reconstruct/predict the dynamic evolution of the flow systems. The POD coefficients at every time step under the condition of a set of parameters are approximated through interpolation with the radial basis function method from those obtained from the snapshots of the chosen parameter space. Hence, the POD coefficients at a set of given time and parameters can be approximated, and the spatial distribution of the solution data can be reconstructed. The current reduced-order model has been applied to the problems governed by a set of parametrized unsteady Navier-Stokes and heat conduction equations. The model capability has been illustrated numerically by three numerical test cases: flow past a cylinder, melt solidification, and dam break. The model prediction capabilities have been evaluated by varying the material properties (viscosity and density) and the heat transfer conditions on some of the boundaries. An error analysis is also carried out to show the model prediction accuracy.