An improved KGF‐SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows. (3rd December 2015)

• Record Type: Journal Article
• Authors: Huang, C.; Lei, J. M.; Liu, M. B.; Peng, X. Y.
• Is Part Of: International journal for numerical methods in fluids. Volume 81:Number 6(2016)
• Page Start: 377
• Page End: 396
• Publication Date: 2015-12-03
• Subjects: smoothed particle hydrodynamics (SPH) -- finite particle method (FPM) -- kernel gradient free (KGF) -- Laplacian operator -- Lagrange -- Euler; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4191
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF‐SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF‐SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF‐SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF‐SPH method avoids nested approximation of first order derivatives, and keeps the good feature of 'kernel gradient free'. The two‐dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF‐SPH and improved KGF‐SPH. The numerical results show that the improved KGF‐SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF‐SPH. Copyright © 2015 John Wiley & Sons, Ltd. Abstract : In this paper, an improved kernel gradient free (KGF)‐smoothed particle hydrodynamics (SPH) method with a novel discrete scheme of Laplacian operator is presented for modeling viscous, incompressible fluid flows. Improved KGF‐SPH method avoids nested approximation of first‐order derivatives, and keeps the good feature of 'KGF'. The 2D incompressible flows of lid‐driven shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, original and improved KGF‐SPH. As shown in the figure (pressure coefficient profiles along upper wall for a lid‐driven shear cavity problem), improved KGF‐SPH with the novel discrete scheme of Laplacian operator is more accurate and stable than SPH, FPM and original KGF‐SPH.