Solution-based adaptive mesh redistribution applied to harmonic balance solvers

Abstract

A primary source of inaccuracy in numerical simulations is due to errors that are introduced into the solution via the discretization of the continuous governing equations over the computational domain. By increasing the grid resolution in regions with high flow gradients and large curvatures using a solution-adaptive approach, these discretization errors can be reduced. In this paper, an adaptive mesh technique is presented that can efficiently cluster the grid nodes in sensitive regions by redistribution and relocation of the grid nodes. This adaptive technique is specifically important to unsteady periodic flow cases where the length scales of the flow features (such as shocks, boundary layer, and separation zones) can differ between time instances. The proposed technique is developed – for the first time in the literature – for a harmonic balance method to efficiently model unsteady periodic flows. To study the performance of the proposed technique in improving the accuracy of the flow solver, steady and unsteady flow cases are studied. Numerical results show that the adaptive mesh redistribution technique is capable of efficiently increasing the accuracy of the numerical solver with a relatively low computational overhead.