A novel 2D algorithm for fluid solid interaction based on the smoothed particle hydrodynamics (SPH) method

Migration of Gas in Water Saturated Clays by Coupled Hydraulic-Mechanical Model

“…A good agreement between the SPH simulations of two-phase flow and micromodel experiments was reported in [24]. It was also demonstrated [25,26] that SPH is capable of simulating elastic media and that solid-fluid interactions can be relatively easily coupled in the framework of the same approach [27][28][29][30]. An interesting feature of the SPH method is its almost local character, which makes it an ideal choice for massively parallel computing, for example, with Compute Unified Device Architecture (CUDA) on Graphics Processing Units (GPU).…”

“…The most frequently used method to model elastic bodies by means of SPH consists in integration of rate of change of the deviatoric stress tensor [25,26,[28][29][30] in the framework of the hypoelastic constitutive model. Another approach consists in calculation of elastic forces from expansion of the elastic strain energy [46,47].…”

“…Interaction of the fluid phase described by SPH with solid objects can be obtained in various ways. Boundary forces taking into account viscous stress and fluid pressure are described in [49,50]; coupling of SPH fluid with rigid solid bodies can be found in [27], while coupling with deformable solids is considered in [51]; coupled models where both the fluid and elastic solid are described in terms of SPH can be found in [28][29][30]. SPH particles belonging to two different phases or two different objects of the same phase are considered as boundary particles if the distance between them is smaller than smoothing length ℎ. Interaction between these particles is defined by the boundary conditions described in Section 2.3.…”

“…In our model, we adopted the simplest way to satisfy the conditions (29) and (30) at the solid-viscous fluid interface by extending the summation in momentum conservation equations for all types of interacting particles [29]. For nonviscous fluid (the viscosity is equal to zero) a more complicated approach is necessary [27,29].…”

“…In our model, we implement the XSPH correction which is a frequently used technique [25,28,30,41] allowing the significant increase in the simulations stability and decrease in nonphysical noisy fluctuations. It consists in using the corrected velocityk for update of the SPH particles positions in the adopted numerical integration scheme instead of the usual particle velocity k which is used in the momentum equation.…”