12 research outputs found
Numerical Equivalence Between SPH and Probabilistic Mass Transfer Methods for Lagrangian Simulation of Dispersion
Several Lagrangian methodologies have been proposed in recent years to
simulate advection-dispersion of solutes in fluids as a mass exchange between
numerical particles carrying the fluid. In this paper, we unify these
methodologies, showing that mass transfer particle tracking (MTPT) algorithms
can be framed within the context of smoothed particle hydrodynamics (SPH),
provided the choice of a Gaussian smoothing kernel whose bandwidth depends on
the dispersion and the time discretization. Numerical simulations are performed
for a simple dispersion problem, and they are compared to an analytical
solution. Based on the results, we advocate for the use of a kernel bandwidth
of the size of the characteristic dispersion length ,
at least given a "dense enough" distribution of particles, for in this case the
mass transfer operation is not just an approximation, but in fact the exact
solution, of the solute's displacement by dispersion in a time step
Numerical equivalence between SPH and probabilistic mass transfer methods for Lagrangian simulation of dispersion
Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length at least given a “dense enough” distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute’s displacement by dispersion in a time step.Peer Reviewe