Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations. (arXiv:1902.00867v2 [cs.NA] UPDATED)
To increase the reliability of simulations by particle methods for
incompressible viscous flow problems, convergence studies and improvements of
accuracy are considered for a fully explicit particle method for incompressible
Navier--Stokes equations. The explicit particle method is based on a penalty
problem, which converges theoretically to the incompressible Navier--Stokes
equations, and is discretized in space by generalized approximate operators
defined as a wider class of approximate operators than those of the smoothed
particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods.
By considering an analytical derivation of the explicit particle method and
truncation error estimates of the generalized approximate operators, sufficient
conditions of convergence are conjectured.Under these conditions, the
convergence of the explicit particle method is confirmed by numerically
comparing errors between exact and approximate solutions. Moreover, by focusing
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