Towards pseudo-spectral incompressible smoothed particle hydrodynamics (ISPH)

Border mapping multi-resolution (BMMR) technique for incompressible projection-based particle methods

“…The solution of the PPE linear system by using iterative solvers is the most time-consuming task of incompressible projection-based particle methods (Hori, et al, 2011;Fernandes, et al, 2015;Chow, et al, 2018;Guo, et al, 2018;Chen & Wan, 2019;Fourtakas, et al, 2021). To evaluate the performance of the present multi-resolution scheme in reducing the runtime to solve the PPE linear system, 2D inviscid standing wave problems, of which the main dimensions are the same used in Section 4.1, as shown in Figure 11, were simulated using different proportions of coarse and fine resolutions.…”

A QSFDI based Laplacian discretisation for modelling wave-structure interaction using ISPH

“…Such superiorities may be limited by the range of the applications and considerable developments have been done to improve the computational performance of ISPH. Typical examples include the Higher order Source term (HS), Higher order Laplacian (HL), Error Compensating Source (ECS), Dynamic Stabilizer (DS) and pressure Gradient Correction (GC) (Khayyer et al, 2017a), the corrected Taylor series consistent pressure gradient models Eulerian-Lagrangian ISPH (Fourtakas et al, 2018), background mesh scheme (Wang et al, 2019), symmetric SPH (SSPH) method (Zhang and Batra, 2009), pseudo-spectral incompressible smoothed particle hydrodynamics (FFT-ISPH) (Rogers et al, 2021) and the implicit consistency correction scheme (Sibilla, 2015). It is also widely recognized that numerical schemes to discretize the PPE, including the Laplacian operator, are critical for securing a satisfactory accuracy, convergence and robustness of the ISPH.…”