Parametric reduced order modeling-based discrete velocity method for simulation of steady rarefied flows

Abstract

In this work, a parametric reduced order modeling-based discrete velocity method (PROM-DVM) is developed for simulation of steady rarefied flows. This method aims to reduce the number of discrete velocity points so as to improve the computational efficiency of DVM. For solving similar problems with different initial parameters, the developed method can generate a sought-after reduced discrete velocity space for the target parameter value from some pre-computed cases and solve the Boltzmann equation directly in the reduced discrete velocity space. At first, the singular-value decomposition (SVD) method is used to find the reduced-order bases for the cases of pre-computed parameter values and the reduced-order basis for the target parameter value is then constructed from the pre-computed bases by the interpolation method based on the Grassmann manifold and its tangent space. The reduced discrete velocity space and its connection to the original discrete velocity space are further established by the discrete empirical interpolation method (DEIM) based on the interpolated reduced-order basis. Since most points in the original discrete velocity space which are of negligible importance are removed in the computation of the present method, a marked improvement in computational efficiency with respect to the DVM in the original discrete velocity space is achieved. Numerical results show that the PROM-DVM can reach 13 times speed-up in CPU time for lid-driven cavity flow.