Theoretical Analysis of the No-Slip Boundary Condition Enforcement in SPH Methods

The aim of the present work is to provide an in-depth analysis of the most representative mirroring techniques used in SPH to enforce boundary conditions (BC) along solid profiles. We specifically refer to dummy particles, ghost particles, and Takeda et al. [Prog. Theor. Phys. 92 (1994), 939] boundary integrals. The analysis has been carried out by studying the convergence of the first- and second-order differential operators as the smoothing length (that is, the characteristic length on which relies the SPH interpolation) decreases. These differential operators are of fundamental importance for the computation of the viscous drag and the viscous/diffusive terms in the momentum and energy equations. It has been proved that close to the boundaries some of the mirroring techniques leads to intrinsic inaccuracies in the convergence of the differential operators. A consistent formulation has been derived starting from Takeda et al. boundary integrals (see the above reference). This original formulation allows implementing no-slip boundary conditions consistently in many practical applications as viscous flows and diffusion problems.

Performance of pressure control valves and flow meters precision in operational irrigation-water balance accuracy

In pressure irrigation-water distribution networks, pressure regulating devices for controlling the discharged flow rate by irrigation units are needed due to the variability of flow rate. In addition, applied water volume is used controlled operating the valve during a calculated time interval, and assuming constant flow rate. In general, a pressure regulating valve PRV is the commonly used pressure regulating device in a hydrant, which, also, executes the open and close function. A hydrant feeds several irrigation units, requiring a wide range in flow rate. In addition, some flow meters are also available, one as a component of the hydrant and the rest are placed downstream. Every land owner has one flow meter for each group of field plots downstream the hydrant. Its lecture could be used for refining the water balance but its accuracy must be taken into account. Ideal PRV performance would maintain a constant downstream pressure. However, the true performance depends on both upstream pressure and the discharged flow rate. The objective of this work is to asses the influence of the performance on the applied volume during the whole irrigation events in a year. The results of the study have been obtained introducing the flow rate into a PRV model. Variations on flow rate are simulated by taking into account the consequences of variations on climate conditions and also decisions in irrigation operation, such us duration and frequency application. The model comprises continuity, dynamic and energy equations of the components of the PRV.

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

Variable-density jet flows induced by concentrated sources of momentum and energy

The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations

Energy-consistent time integration for nonlinear viscoelasticity

This work is concerned with the numerical solution of the evolution equations of thermomechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided