Development of computationally efficient augmented Lagrangian SPH for incompressible flows and its quantitative comparison with WCSPH simulating flow past a circular cylinder

Abstract

SummaryIn Lagrangian particle‐based methods such as smoothed particle hydrodynamics (SPH), computing totally divergence‐free velocity field in a flow domain with the smallest error possible is the most critical issue, which might be achieved through solving pressure Poisson equation implicitly with higher particle resolutions. However, implicit solutions are computationally expensive and may be particularly challenging in the solution of multiphase flows with highly nonlinear deformations as well as fluid‐structure interaction problems. Augmented Lagrangian SPH (ALSPH) method is a new alternative algorithm as a prevalent pressure solver where the divergence‐free velocity field is achieved by iterative calculation of velocity and pressure fields. This study investigates the performance of the ALSPH technique by solving a challenging flow problem such as two‐dimensional flow around a cylinder within the Reynolds number range of 50 to 500 in terms of improved robustness, accuracy, and computational efficiency. The same flow conditions are also simulated using the conventional weakly compressible SPH (WCSPH) method. The results of ALSPH and WCSPH solutions are not only compared in terms of numerical validation/verification studies, but also rigorous investigations are performed for all related physical flow characteristics, namely, hydrodynamic coefficients, frequency domain analyses, and velocity divergence fields.

The Effect of Iterative Procedures on the Robustness and Fidelity of Augmented Lagrangian SPH

“…Moreover, in order to reduce the computational costs, explicit incompressible SPH formulations are also present in the literature [22][23][24], which introduce simplifying assumptions for solving the pressure Poisson equation in an explicit fashion. Augmented Lagrangian SPH (ALSPH) is the most recent and novel explicit incompressible SPH method that has been recently introduced and further improved by the authors [25,26].…”

“…Fatehi et al [25] performed simulations with the ALSPH method on 2D flow over the backward facing step and 2D pressure jump problems, when comparing the results with the weakly compressible SPH (WCSPH) method. In our recent study [26], along with algorithm enhancements and a simple adaptive scheme for the penalty term estimation, we have further investigated the performance of the ALSPH method through solving a challenging incompressible flow problem, namely, 2D flow past a circular cylinder under low to moderate Reynolds numbers. The authors [25,26] demonstrated the advantage of ALSPH over WCSPH in terms of rendering smoother pressure fields and smaller velocity divergences at the expense of a larger computational cost.…”

“…In our recent study [26], along with algorithm enhancements and a simple adaptive scheme for the penalty term estimation, we have further investigated the performance of the ALSPH method through solving a challenging incompressible flow problem, namely, 2D flow past a circular cylinder under low to moderate Reynolds numbers. The authors [25,26] demonstrated the advantage of ALSPH over WCSPH in terms of rendering smoother pressure fields and smaller velocity divergences at the expense of a larger computational cost. The findings of our study [26] have further indicated the accuracy of the ALSPH method, especially in higher Reynolds numbers, as compared to the WCSPH method at same particle resolutions and time step sizes.…”

“…The authors [25,26] demonstrated the advantage of ALSPH over WCSPH in terms of rendering smoother pressure fields and smaller velocity divergences at the expense of a larger computational cost. The findings of our study [26] have further indicated the accuracy of the ALSPH method, especially in higher Reynolds numbers, as compared to the WCSPH method at same particle resolutions and time step sizes. In our previous study [26], the effects of the time step size or the maximum number of iterations per time step were not investigated.…”

“…In our previous study [26], the effects of the time step size or the maximum number of iterations per time step were not investigated. When considering higher particle resolution requirements of the WCSPH method at higher Reynolds numbers [34][35][36], our results have also pointed out the advantage of the ALSPH method over WCSPH in terms of computational costs, even without optimizing these temporal and iterative discretization parameters [26].…”