Abstract

The Finite Particle Method (FPM) and the Decoupled Finite Particle Method (DFPM) are variants of the Smoothed Particle Hydrodynamics (SPH) in which the estimation of a field and its gradient for an arbitrary distribution of particles is performed by imposing first order consistency equations (C-1). A modification of the kernel is introduced that involves the inversion of a correction matrix for each interpolation point in the system. In the FPM, the inversion is rigorously performed and therefore the method has first-order consistency (C-1). However, in DPFM the vanishingly small non-diagonal terms in the correction matrix are neglected to obtain a more straightforward method, at expense of consistency. Following the idea of DFPM, the Semi-Decoupled Finite Particle Method (SDFPM) and the Corrected Semi Decoupled Finite Particle Method (CSDFPM) are introduced. In the SDFPM, the kernel is normalized by a Shepard factor and the first order consistency equations are solved by neglecting non-diagonal terms in the correction matrix as in the DFPM method. In the corrected version of this method (CSDFPM), the SDFPM estimation is used as the initial guess to get a second corrected estimation in the C-1 equations. The precision of FPM, DFPM, SDFPM, and CSDFPM is tested by evaluating the gradient components of a field around a cylindrical obstacle and around a cylindrical hole by using (i) trial field functions with an ordered array of particles and (ii) the pressure field with a distribution of particles taken from a flow simulation. Drag coefficients for flow around a cylinder are obtained by the different methods and compared in a wide range of Reynolds numbers, including the laminar and turbulent regimes. The gradient components and drag coefficients calculated with the proposed methods show a precision comparable to the FPM at a lower computational cost. (C) 2020 Elsevier Inc. All rights reserved.