Semi‐analytical smoothed‐particle hydrodynamics correction factors for polynomial kernels and piecewise‐planar boundaries

Abstract

This work presents a method of exactly and efficiently evaluating integrals of compactly supported (and otherwise) polynomial radial kernels near piecewise-planar boundaries. The technique is motivated by and has an immediate application in the smoothed-particle hydrodynamics method employing the semi-analytical boundary formulation. The current implementation is exact and fully general, avoiding any need for symbolic or numerical integration which previous implementations rely on. A detailed derivation and three compact implementations are provided and the latter can be easily modified to fit new and existing simulation codes. Applications and good performance are demonstrated on a number of test problems, where the semi-analytical boundary method can simulate complex boundaries using roughly half the boundary particles required in a ghost particle boundary method.

PolyMPS—An open source CFD solver based on Polygon walls in Moving Particle Semi-implicit (MPS) method

“…• Boundary walls represented by a scalar field with discrete signed distance functions (SDF) [28], aiming to improve the efficiency in calculate the distances between the particles and mesh. • Accuracy improvement of the polygon wall formalism by adopting numerical boundary integrations [29], semi-analytical boundary integrations [30] or analytical volume integrations [31]. • Inclusion of multi-resolution techniques (see Table 1 in [32]) should also be evaluated with respect to adaptivity and versatility of our code.…”

Contact framework for total Lagrangian smoothed particle hydrodynamics using an adaptive hybrid kernel scheme

“…The method enhances the SPH and allows the definition of the boundary condition directly. In other work, 26 a semi‐analytical boundary formulation was proposed, which can evaluate the exact integrals of compactly support polynomial radial kernels near piecewise‐planar boundaries efficiently. A strategy to preserve the energy in a consistent basis function was proposed, in which the correction term at every interaction pair is implemented to achieve local energy conservation 27 .…”