2-D numerical modeling of rapidly varying shallow water flows by Smoothed Particle Hydrodynamics technique

River engineeringNumerical modelling in river engineerin

Implicit iterative particle shifting for meshless numerical schemes using kernel basis functions

A novel particle shifting technique (PST) for meshless numerical methods is presented. The proposed methodology uses an implicit iterative particle shifting (IIPS) technique aiming to reduce the spatial particle’ anisotropy, which is associated with the discretization error in meshless numerical schemes based on kernel basis functions. The algorithm controls the particle spatial distribution through an implicit minimization problem, related to the particle concentration gradient and therefore, to the particles’ anisotropy. This results in accurate particle distributions, to demonstrate the effectiveness of the proposed method, the IIPS algorithm is tested within a smoothed particle hydrodynamics (SPH) framework, with static and kinematic cases, by examining the particle distributions and the corresponding spatial accuracy. Further, the computational cost of the proposed methodology is reported and it is shown that it introduces minimal overhead. Moreover, the simulations of the Taylor–Green vortex (TGV), employing a weakly-compressible SPH Navier–Stokes solver, confirmed the superior accuracy of the IIPS in comparison to existing explicit shifting approaches, in simulating internal flows

DualSPHysics: from fluid dynamics to multiphysics problems

DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier–Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics especially suited for the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single-phase simulations, allowing multi-phase simulations with gas–liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics an advanced meshless solver with emphasis on free-surface flow modelling

Divergence cleaning for weakly compressible smoothed particle hydrodynamics

This paper presents a divergence cleaning formulation for the velocity in the weakly compressible smoothed particle hydrodynamics (SPH) scheme. The proposed hyperbolic/parabolic divergence cleaning, ensures that the velocity divergence, div(u), is minimised throughout the simulation. The divergence equation is coupled with the momentum conservation equation through a scalar field ψ. A parabolic term is added to the time-evolving divergence equation, resulting in a hyperbolic/parabolic form, dissipating acoustic waves with a speed of sound proportional to the local Mach number in order to maximise dissipation of the velocity divergence, preventing unwanted diffusion of the pressure field. The div(u)-SPH algorithm is implemented in the open-source weakly compressible SPH solver DualSPHysics. The new formulation is validated against a range of challenging 2-D test cases including the Taylor-Green vortices, patch impact test, jet impinging on a surface, and wave impact in a sloshing tank. The results show that the new formulation reduces the divergence in the velocity field by at least one order of magnitude which prevents spurious numerical noise and the formation of unphysical voids. The temporal evolution of the impact pressures shows that the div(u)-SPH formulation virtually eliminates unwanted acoustic pressure oscillations. Investigation of particle resolution confirms that the new div(u)-SPH formulation does not reduce the spatial convergence rate

Qualitative structure-metabolism relationships in the hydrolysis of carbamates.

The aims of this review were 1) to compile a large number of reliable literature data on the metabolic hydrolysis of medicinal carbamates and 2) to extract from such data a qualitative relation between molecular structure and lability to metabolic hydrolysis. The compounds were classified according to the nature of their substituents (R³OCONR&supl;R²), and a metabolic lability score was calculated for each class. A trend emerged, such that the metabolic lability of carbamates decreased (i.e., their metabolic stability increased), in the following series: Aryl-OCO-NHAlkyl >> Alkyl-OCO-NHAlkyl ~ Alkyl-OCO-N(Alkyl)? ? Alkyl-OCO-N(endocyclic) ? Aryl-OCO-N(Alkyl)? ~ Aryl-OCO-N(endocyclic) ? Alkyl-OCO-NHAryl ~ Alkyl-OCO-NHAcyl?>> Alkyl-OCO-NH? > Cyclic carbamates. This trend should prove useful in the design of carbamates as drugs or prodrugs

Ibn Shuhayd and his Risalat at-tawabi' wa-z-zawabi'

The solution for the shallow water equations using smoothed particle hydrodynamics is attractive, being a mesh-free, automatically adaptive method without special treatment for wet–dry interfaces. However, the relatively new method is limited by the variable kernel size or smoothing length being inversely proportional to water depth causing poor resolution at small depths. Boundary conditions at solid walls have also not been well resolved. To solve the resolution problem in small depths, a particle splitting procedure was developed (conveniently into seven particles), which conserves mass and momentum by varying the smoothing length, velocity and acceleration of each refined particle. This improves predictions in the shallowest depths where the error associated with splitting is reduced by one order of magnitude in comparison to other published works. To provide good shock capturing behaviour, particle interactions are treated as a Riemann problem with Monotone Upstream-centred Scheme for Conservation Laws (MUSCL) reconstruction providing stability. For solid boundaries, the recent modified virtual boundary particle method was developed further to enable the zeroth moment to be accurately conserved where the smoothing length of particles is changing rapidly during particle splitting. The resulting method is applied to the one-dimensional and the two-dimensional axisymmetric wet-bed dam break problems showing close agreement with analytical solutions, demonstrating the need for particle splitting. To demonstrate wetting and drying in a more complex case, the scheme is applied to oscillating water in a two-dimensional parabolic basin and produces good agreement with the analytical solution. The method is finally applied to the European Concerted Action on DAm break Modelling dam-break test case representative of realistic conditions and good predictions are made of experimental measurements with a 40% reduction in the computational time when particle splitting is employed. The overall method has thus become quite sophisticated but its generality and versatility will be attractive for various shallow water problem

Shallow water SPH for flooding with dynamic particle coalescing and splitting

In this paper an adaptive algorithm for Smoothed Particle Hydrodynamics (SPH) for the Shallow Water Equations (SWEs) is presented. The area of a particle is inversely proportional to depth giving poor resolution in small depths without particle refinement. This is a particular limitation for flooding problems of interest here. Higher resolution is created by splitting the particles, while particle coalescing (or merging) improves efficiency by reducing the number of the particles when acceptable. The new particle coalescing procedure merges two particles together if their area becomes less than a predefined threshold value. Both particle splitting and coalescing procedures conserve mass and momentum and the smoothing length of new particles is calculated by minimizing the density error of the SPH summation. The new dynamic particle refinement procedure is assessed by testing the numerical scheme against analytical, experimental and benchmark test cases. The analytical cases show that with particle splitting and coalescing typical convergence rates remain faster than linear. For the practical test case, in comparison to using particle splitting alone, the particle coalescing procedure leads to a significant reduction of computational time, by a factor of 15. This makes the computational time of the same order as mesh-based methods with the advantage of not having to specify a mesh over a flood domain of unknown extent a priori

A correction for balancing discontinuous bed slopes in two-dimensional smoothed particle hydrodynamics shallow water modeling

In this paper, a smoothed particle hydrodynamics (SPH) numerical model for the shallow water equations (SWEs) with bed slope source term balancing is presented. The solution of the SWEs using SPH is attractive being a conservative, mesh-free, automatically adaptive method without special treatment for wet-dry interfaces. Recently, the capability of the SPH-SWEs numerical scheme with shock capturing and general boundary conditions has been used for predicting practical flooding problems. The balance between the bed slope source term and fluxes in shallow water models is desirable for reliable simulations of flooding over bathymetries where discontinuities are present and has received some attention in the framework of Finite Volume Eulerian models. The imbalance because of the source term resulting from the calculation of the the water depth is eradicated by means of a corrected mass, which is able to remove the error introduced by a bottom discontinuity. Two different discretizations of the momentum equation are presented herein: the first one is based on the variational formulation of the SWEs in order to obtain a fully conservative formulation, whereas the second one is obtained using a non-conservative form of the free-surface elevation gradient. In both formulations, a variable smoothing length is considered. Results are presented demonstrating the corrections preserve still water in the vicinity of either 1D or 2D bed discontinuities and provide close agreement with 1D analytical solutions for rapidly varying flows over step changes in the bed. The method is finally applied to 2D dam break flow over a square obstacle where the balanced formulation improves the agreement with experimental measurements of the free surface. ?? 2012 John Wiley & Sons, Ltd