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Discretization correction of general integral PSE operators for particle methods. (English) Zbl 1334.65196

Summary: The general integral particle strength exchange (PSE) operators [J. D. Eldredge, A. Leonard and T. Colonius, J. Comput. Phys. 180, No. 2, 686–709 (2002; Zbl 1143.76550)] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.

MSC:

65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
74S20 Finite difference methods applied to problems in solid mechanics
76M28 Particle methods and lattice-gas methods

Citations:

Zbl 1143.76550

Software:

Matlab; LAPACK
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References:

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