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The aim of the paper is to introduce a random elastic traffic equilibrium problem in a Hilbert space setting. The equilibrium condition is expressed by a random extension of the elastic Wardrop principle. Its characterization with a stochastic quasi-variational inequality is proved. Under suitable assumptions, the existence of a random equilibrium distribution is established. Furthermore, a numerical scheme to compute the random elastic traffic equilibrium distribution is presented. Finally a numerical example is discussed. [ABSTRACT FROM AUTHOR]

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray–Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs so that the method only requires samples of the field at (possibly scattered) nodes over the domain. Numerical results are presented demonstrating high-order convergence in both space (between 5th and 6th orders) and time (up to 4th order) for some model problems in two dimensional irregular geometries. [ABSTRACT FROM AUTHOR]

In this paper the numerical integration of non conservative perturbations of differential systems that possess a first integral, as for example slowly dissipative Hamiltonian systems, is considered. Numerical methods that are able to reproduce appropriately the evolution of the first integral are proposed. These algorithms are based on a combination of standard numerical integration methods and certain projection techniques. Some conditions under which known conservative methods reproduce that desirable evolution in the invariant are analysed. Finally, some numerical experiments in which we compare the behaviour of the new proposed methods, the averaged vector field method AVF proposed by Quispel and McLaren and standard RK methods of orders 3 and 5 are presented. The results confirm the theory and show a good qualitative and quantitative performance of the new projection methods. [ABSTRACT FROM AUTHOR]

Highlights: [•] Low-dissipative LES/DNS flow solvers implemented into OpenFOAM. [•] Dissipation properties quantified with four numerical experiments. [•] The Runge–Kutta projection methods are new in OpenFOAM. [•] Solver code syntax, implementation and validation discussed. [•] Speed-up gain as good as 60–70% achieved. [Copyright &y& Elsevier]

Abstract: The analogies between the Moving Particle Semi-implicit method (MPS) and Incompressible Smoothed Particle Hydrodynamics method (ISPH) are established in this note, as an extension of the MPS consistency analysis conducted in Souto-Iglesias et al. (2013). [Copyright &y& Elsevier]

Abstract: In this paper we propose to study open boundary conditions for incompressible Navier–Stokes equations, in the framework of velocity-correction methods. The standard way to enforce this type of boundary condition is described, followed by an adaptation of the one we proposed in [36] that provides higher pressure and velocity convergence rates in space and time for pressure-correction schemes. These two methods are illustrated with a numerical test with both finite volume and spectral Legendre methods. We conclude with three physical simulations: first with the flow over a backward-facing step, secondly, we study, in a geometry where a bifurcation takes place, the influence of Reynolds number on the laminar flow structure, and lastly, we verify the solution obtained for the unsteady flow around a square cylinder. [Copyright &y& Elsevier]

Reverse Osmosis has important applications to seawater desalination and advanced water treatment. Its efficiency depends, however, on unsteady fluid flow and solute transport that are challenging to simulate. The challenges arise due to interactions between solute boundary layers and unsteady vortical flow structures generated by complicated geometries. These flow structures also interact with semi-permeable membranes through which the permeate flow depends on the local pressure. We show that this additional pressure coupling causes the temporal accuracy of traditional projection methods to drop to first-order. We track the source of this accuracy drop to the treatment of viscous terms in the derivation of the Poisson equation used to update the velocity and pressure fields. This allows us to propose a modified projection method that recovers second-order temporal accuracy. Finally, we show that the modified projection method can be coupled to convective outlet conditions and immersed boundary conditions to simulate reverse osmosis in steady and unsteady flow regimes. • Reverse osmosis systems have a unique pressure–velocity coupling that lowers the accuracy of popular projection methods. • The drop in accuracy arises from the treatment of viscous terms. • A modified projection method recovers second order spatial–temporal accuracy. [ABSTRACT FROM AUTHOR]

Skipped correlations are measures of association based on the data left after outliers are removed. Using a projection-type multivariate outlier detection technique, a method for testing the hypothesis of a zero skipped correlation has been found that performs well in simulations when dealing with bivariate data. However, an obvious extension of the method to p-variate data, p>2, fails to control the familywise error rate (the probability of at least one Type I error) under nonnormality. A modification of the method, based in part on Spearman''s correlation, is found to be more satisfactory. [Copyright &y& Elsevier]

In this paper, we present an efficient projection method to solve the three-dimensional time-dependent incompressible Navier–Stokes equations in primitive variables formulation using spectral approximations. This method is based on a modification of the algorithm proposed by Goda [J. Comp. Phys. 30 (1979) 76]. It brings an improvement by introducing a preliminary step for the pressure in order to allow a temporal evolution of the normal pressure gradient at the boundaries. Its efficiency is brought to the fore by comparison with the Goda''s algorithm. The modified projection method is then applied to the simulation of complex three-dimensional flows in rotating cavities, involving either a throughflow or a differential rotation. [Copyright &y& Elsevier]

• DCMD can be simulated using immersed boundaries and projection methods. • The projection method staggers coupled channels and accounts for outlets. • The immersed boundaries apply Neumann conditions to second-order accuracy. Membrane distillation is an emerging desalination process with important applications to the energy-water nexus. Its performance depends, however, on heat and mass transport phenomena that are uniquely challenging to simulate. Difficulties include two adjacent channel flows coupled by heat and mass transport across a semi-permeable membrane. Within the channels, heat and mass boundary layers interact with the membrane surface and vortical flow structures generated by complicated geometries. The presence of multiple inlets and outlets also complicates the application of mass-conserving outlet conditions. Moreover, even small amounts of outlet noise affect the resolution of important near-membrane fluid velocities. We show these phenomena can be simulated to second-order spatial and temporal accuracy using finite volume methods with immersed boundaries and projection methods. Our approach includes a projection method that staggers the coupled channel flows and applies Robin boundary conditions to facilitate mass conservation at the outlets. We also develop an immersed boundary method that applies Neumann boundary conditions to second-order spatial accuracy. The methods are verified and validated against manufactured solutions and theoretical predictions of vortex shedding. They are then applied to the simulation of steady and unsteady transport phenomena in membrane distillation. The methods have important applications to the broad field of chemical engineering and deal with long-standing issues in both theoretical and computational fluid dynamics. [ABSTRACT FROM AUTHOR]