This paper presents a new numerical collocation procedure, based on Cartesian grids and one-dimensional integrated radial-basis-function networks (1D-IRBFNs), for the simulation of natural convection defined in two-dimensional multiply-connected domains and governed by the stream function -vorticity -temperature formulation. Special emphasis is placed on the handling of vorticity values at boundary points that do not coincide with grid nodes. A suitable formula for computing vorticity boundary conditions, which is based on the approximations with respect to one coordinate direction only, is proposed. Normal derivative boundary conditions for the stream function are forced to be satisfied identically. Several test problems, including natural convection in the annulus between square and circular cylinders, are considered to investigate the accuracy of the proposed technique.
This paper reports a radial-basis-function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of high-order derivatives. The method is applied to simulate thermally-driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleighnumber solutions are achieved and they are in good agreement with previously published numerical data.
A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.
Many materials (e.g., gels, colloids, concentrated cohesive sediments, etc.) exhibit a stable solid form at rest, and liquify once subjected to an applied stress exceeding a critical value -a yield-stress behaviour. This can be qualitatively explained by the forming and destruction of the fluid microstructure [1], and it may be modelled as a thixotropic and yield stress material. In this paper, we propose a mesoscopic model which is able to mimic a thixotropic and yield stress behaviour using a particle-based technique known as dissipative particle dynamics (DPD). The DPD technique satisfies conservation of mass and momentum and it has been applied successfully for a number of problems in-
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