A local Lagrangian gradient smoothing method for fluids and fluid-like solids: A novel particle-like method

Abstract

The Lagrangian Gradient Smoothing Method (L-GSM) proposed in our earlier work overcomes effectively the ‘tensile instability’ problem inherently existed in the widely used smoothed particle hydrodynamics (SPH) method. However, the employment of background grid in L-GSM for the construction of gradient smoothing domains leads some drawbacks to the L-GSM framework: low computational efficiency, complex implementation procedure and technical challenges for parallel computing algorithm development. Accordingly, this study proposes a novel particle-like method, termed as local L-GSM (LL-GSM), through constructing gradient smoothing domains locally for LL-GSM particles. The present LL-GSM consists of three unique ingredients: (1) Only locally constructed gradient smoothing domains are used; (2) an efficient localized neighbor-searching algorithm is developed for the search of supporting particles; (3) a simple and effective free surface technique is adopted for accurate application of free surface effect. The accuracy, stability and efficiency of the newly proposed LL-GSM framework are then investigated comprehensively by conducting thorough theoretical and numerical analyses. At last, benchmark problems including two incompressible flows and two free surface flows are used to verify the capability of LL-GSM in handling large deformation of fluids and fluid-like solids. The LL-GSM results are evaluated carefully by comparing with experimental results, theoretical solutions, and numerical solutions. Results comparison demonstrates that the proposed LL-GSM method can give very accurate numerical solutions in all these problems with a much better computational efficiency and easier implementation. It is also evidenced that, same to L-GSM, the LL-GSM is free from the ‘tensile instability’ issue.