Abstract
The smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics. Generally, a high-precision interpolation is required to calculate the particle physical attributes and their derivatives for the boundary treatment and postproceeding in the SPH simulation. However, as a result of the truncation of kernel function support domain and irregular particle distribution, the interpolation using conventional SPH interpolation experiences low accuracy for the particles near the boundary and free surface. To overcome this drawback, stable regularized moving least-squares (SRMLS) method was introduced for interpolation in SPH. The surface fitting studies were performed with a variety of polyline bases, spatial resolutions, particle distributions, kernel functions, and support domain sizes. Numerical solutions were compared with the results using moving least-squares (MLS) and three SPH methods, including CSPH, K2SPH, and KGFSPH, and it was found that SRMLS not only has nonsingular moment matrix, but also obtains high-accuracy result. Finally, the capability of the algorithm coupled with SRMLS and SPH was illustrated and assessed through several numerical tests.
Highlights
Academic Editor: Mohamed Shaat e smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics
Numerical solutions were compared with the results using moving least-squares (MLS) and three SPH methods, including CSPH, K2SPH, and KGFSPH, and it was found that stable regularized moving least-squares (SRMLS) has nonsingular moment matrix, and obtains high-accuracy result
To maintain the stability of SPH simulation, a particle shifting technique [33] was adopted in all simulations. en interpolation in the schemes of boundary treatment, density re-initialization, and postproceeding were dealt with SRMLS with quadratic basis
Summary
Academic Editor: Mohamed Shaat e smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics. As a result of the truncation of kernel function support domain and irregular particle distribution, the interpolation using conventional SPH interpolation experiences low accuracy for the particles near the boundary and free surface. To overcome this drawback, stable regularized moving least-squares (SRMLS) method was introduced for interpolation in SPH. Introduction e smoothed particle hydrodynamics (SPH) method is a Lagrangian meshless method that was developed for the astrophysical flow simulation in 1970s [1, 2] It has been a promising numerical technique for the complex fluid flow simulations as well as for various fields, including thermodynamics and aerodynamics in recent years [3,4,5,6,7]. The moment matrix in MLS may be singular for ill-quality particle sets, several techniques have been proposed to deal with ill-posed least-squares problem such as coordinate transformation, perturbation of nodal position, and matrix triangularization [20,21,22]
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