Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.
This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretization. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretization. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microsesimic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology.
SUMMARYMould ÿlling simulation in high pressure die casting has been an attractive area of research for many years. Several numerical methodologies have been attempted in the past to study the ow behaviour of the molten metal into the die cavities. However, many of these methods require a stationary mesh or grid which limits their ability in simulating highly dynamic and transient ows encountered in high pressure die casting processes. In recent years, the advent of meshfree methods have expanded the capabilities of numerical techniques. Hence, these methods have emerged as an attractive alternative for modelling mould ÿlling simulation in pressure die casting processes. In the present work, a Lagrangian particle method called corrected smooth particle hydrodynamics (CSPH) is used to simulate uid ow in the high pressure die casting cavity. This paper mainly focuses on deriving the fundamental governing equations based on a variational formulation and presents a number of mould ÿlling examples to demonstrate the capabilities of the CSPH numerical model.
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