S. Adami

A generalized wall boundary condition for smoothed particle hydrodynamics

In this paper we present a new formulation of the boundary condition at static and moving solid walls in SPH simulations. Our general approach is both applicable to two and three dimensions and is very simple compared to previous wall boundary formulations. Based on a local force balance between wall and fluid particles we apply a pressure boundary condition on the solid particles to prevent wall penetration. This method can handle sharp corners and complex geometries as is demonstrated with several examples. A validation shows that we recover hydrostatic equilibrium conditions in a static tank, and a comparison of the classical dam break simulation with state-of-the-art results in literature shows good agreement. We simulate various problems such as the flow around a cylinder and the backward facing step at Re=100 to demonstrate the general applicability of this new method.

A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation

In this paper, we propose a new surface-tension formulation for multi-phase smoothed particle hydrodynamics (SPH). To obtain a stable and accurate scheme for surface curvature, a new reproducing divergence approximation without the need for a matrix inversion is derived. Furthermore, we introduce a density-weighted color-gradient formulation to reflect the reality of an asymmetrically distributed surface-tension force. We validate our method with analytic solutions and demonstrate convergence for different cases. Furthermore, we show that our formulation can handle phase interfaces with density and viscosity ratios of up to 1000 and 100, respectively. Finally, complex three-dimensional simulations including breakup of an interface demonstrate the capabilities of our method.

A transport-velocity formulation for smoothed particle hydrodynamics

The standard weakly-compressible SPH method suffers from particle clumping and void regions for high Reynolds number flows and when negative pressures occur in the flow. As a remedy, a new algorithm is proposed that combines the homogenization of the particle configuration by a background pressure while at the same time reduces artificial numerical dissipation. The transport or advection velocity of particles is modified and an effective stress term occurs in the momentum balance that accounts for the difference between advection velocity times particle density and actual particle momentum. The present formulation can be applied for internal flows where the density summation is applicable. A wide range of test cases demonstrates unprecedented accuracy and stability of the proposed modification even at previously infeasible conditions.

A conservative SPH method for surfactant dynamics

In this paper, a Lagrangian particle method is proposed for the simulation of multiphase flows with surfactant. The model is based on the multiphase smoothed particle hydrodynamics (SPH) framework of Hu and Adams (2006) [1]. Surface-active agents (surfactants) are incorporated into our method by a scalar quantity describing the local concentration of molecules in the bulk phase and on the interface. The surfactant dynamics are written in conservative form, thus global mass of surfactant is conserved exactly. The transport model of the surfactant accounts for advection and diffusion. Within our method, we can simulate insoluble surfactant on an arbitrary interface geometry as well as interfacial transport such as adsorption or desorption. The flow-field dynamics and the surfactant dynamics are coupled through a constitutive equation, which relates the local surfactant concentration to the local surface-tension coefficient. Hence, the surface-tension model includes capillary and Marangoni-forces. The present numerical method is validated by comparison with analytic solutions for diffusion and for surfactant dynamics. More complex simulations of an oscillating bubble, the bubble deformation in a shear flow, and of a Marangoni-force driven bubble show the capabilities of our method to simulate interfacial flows with surfactants.