An algorithm to improve consistency in Smoothed Particle Hydrodynamics. (2nd September 2015)

• Record Type: Journal Article
• Authors: Sibilla, Stefano
• Is Part Of: Computers & fluids. Volume 118(2015)
• Page Start: 148
• Page End: 158
• Publication Date: 2015-09-02
• Subjects: Smoothed Particle Hydrodynamics (SPH) -- Meshless methods -- Lagrangian methods -- Consistency restoration; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2015.06.012
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: An algorithm to improve the accuracy of derivatives in 1D SPH is proposed. A linear system for the first 3 derivatives is solved at each particle location. Second-order consistency on the first derivative is obtained everywhere. First-order consistency on the second derivative is obtained everywhere. Tests on Burgers equation confirm applicability to convection–diffusion problems. Abstract: An algorithm to improve the numerical evaluation of derivatives of a field function in Smoothed Particle Hydrodynamics is proposed. The algorithm is based on the solution, at each particle location, of a linear system whose unknowns are the first three derivatives of the desired function; the coefficients of the linear system are obtained from various possible particle approximations of the Taylor series expansion of the function. The method proves to be 2nd-order consistent for the 1st derivatives and 1st-order consistent for the 2nd derivatives, both inside the domain and close to the boundaries, and it is not affected by an irregular particle distribution. A numerical test performed on the SPH solution of the viscous Burgers equation proves that the method can be validly applied to the simulation of convection–diffusion problems.