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.
An algorithm to improve consistency in Smoothed Particle Hydrodynamics
SIBILLA, STEFANO
2015-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
