Constraint-consistent Runge-Kutta methods for one-dimensional incompressible multiphase flow

New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the mass and momentum equations and implicit for the volume constraint. These half-explicit methods are constraint-consistent, i.e., they satisfy the hidden constraints of the two-fluid model, namely the volumetric flow (incompressibility) constraint and the Poisson equation for the pressure. A novel analysis shows that these hidden constraints are present in the continuous, semi-discrete, and fully discrete equations. Next to constraint-consistency, the new methods are conservative: the original mass and momentum equations are solved, and the proper shock conditions are satisfied; efficient: the implicit constraint is rewritten into a pressure Poisson equation, and the time step for the explicit part is restricted by a CFL condition based on the convective wave speeds; and accurate: achieving high order temporal accuracy for all solution components (masses, velocities, and pressure). High-order accuracy is obtained by constructing a new third order Runge-Kutta method that satisfies the additional order conditions arising from the presence of the constraint in combination with time-dependent boundary conditions. Two test cases (Kelvin-Helmholtz instabilities in a pipeline and liquid sloshing in a cylindrical tank) show that for time-independent boundary conditions the half-explicit formulation with a classic fourth-order Runge-Kutta method accurately integrates the two-fluid model equations in time while preserving all constraints. A third test case (ramp-up of gas production in a multiphase pipeline) shows that our new third order method is preferred for cases featuring time-dependent boundary conditions

The Purpose of the Corporation

Paige Morrow and Jeroen Veldman report on the findings of a major global project to identify how companies can create long-term sustainable value

Global and local conservation of mass, momentum and kinetic energy in the simulation of compressible flow

The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions are sought for the local and global conservation of primary (mass and momentum) and secondary (kinetic energy) invariants on Cartesian meshes. The analysis, based on a matrix approach, shows that sharp criteria for global and local conservation can be obtained and that in many cases these two concepts are equivalent. Explicit numerical fluxes are derived in all finite-difference formulations for which global conservation is guaranteed, even for non-uniform Cartesian meshes. The treatment reveals also an intimate relation between conservative finite-difference formulations and cell-centered finite-volume type approaches. This analogy suggests the design of wider classes of finite-difference discretizations locally preserving primary and secondary invariants

Parabolic interface reconstruction for 2D volume of fluid methods

For capillary driven flow the interface curvature is essential in the modelling of surface tension via the imposition of the Young–Laplace jump condition. We show that traditional geometric volume of fluid (VOF) methods, that are based on a piecewise linear approximation of the interface, do not lead to an interface curvature which is convergent under mesh refinement in time-dependent problems. Instead, we propose to use a piecewise parabolic approximation of the interface, resulting in a class of piecewise parabolic interface calculation (PPIC) methods. In particular, we introduce the parabolic LVIRA and MOF methods, PLVIRA and PMOF, respectively. We show that a Lagrangian remapping method is sufficiently accurate for the advection of such a parabolic interface. It is numerically demonstrated that the newly proposed PPIC methods result in an increase of reconstruction accuracy by one order, convergence of the interface curvature in time-dependent advection problems and Weber number independent convergence of a droplet translation problem, where the advection method is coupled to a two-phase Navier–Stokes solver. The PLVIRA method is applied to the simulation of a 2D rising bubble, which shows good agreement to a reference solution.</p

Branching of the Falkner-Skan solutions for λ < 0

The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.

Age-dependent modulation of motor network connectivity for skill acquisition, consolidation and interlimb transfer after motor practice

Objective: Age-related differences in neural strategies for motor learning are not fully understood. We determined the effects of age on the relationship between motor network connectivity and motor skill acquisition, consolidation, and interlimb transfer using dynamic imaging of coherent sources. Methods: Healthy younger (n = 24, 18-24 y) and older (n = 24, 65-87 y) adults unilaterally practiced a visuomotor task and resting-state electroencephalographic data was acquired before and after practice as well as at retention. Results: The results showed that right-hand skill acquisition and consolidation did not differ between age groups. However, age affected the ability to transfer the newly acquired motor skill to the non-practiced limb. Moreover, strengthened left- and right-primary motor cortex-related beta conectivity was negatively and positively associated with right-hand skill acquisition and left-hand skill consolidation in older adults, respectively. Conclusion: Age-dependent modulations of bilateral resting-state motor network connectivity indicate age-specific strategies for the acquisition, consolidation, and interlimb transfer of novel motor tasks. Significance: The present results provide insights into the mechanisms underlying motor learning that are important for the development of interventions for patients with unilateral injuries. (C) 2021 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved

Motor Skill Acquisition and Retention after Somatosensory Electrical Stimulation in Healthy Humans

Somatosensory electrical stimulation (SES) can increase motor performance, presumably through a modulation of neuronal excitability. Because the effects of SES can outlast the period of stimulation, we examined the possibility that SES can also enhance the retention of motor performance, motor memory consolidation, after 24 hours (Day 2) and 7 days (Day 7), that such effects would be scaled by SES duration, and that such effects were mediated by changes in aspects of corticospinal excitability, short-interval intracortical inhibition (SICI), and intracortical facilitation (ICF). Healthy young adults (n = 40) received either 20 (SES-20), 40 (SES-40), or 60 minutes (SES-60) of real SES, or sham SES (SES-0). The results showed SES-20 increased visuomotor performance on Day 2 (15%) and Day 7 (17%) and SES-60 increased visuomotor performance on Day 7 (11%; all p < 0.05) compared with SES-0. Specific responses to transcranial magnetic stimulation (TMS) increased immediately after SES (p < 0.05) but not on Days 2 and 7. In addition, changes in behavioral and neurophysiological parameters did not correlate, suggesting that paths and structures other than the ones TMS can assay must be (also) involved in the increases in visuomotor performance after SES. As examined in the present study, low-intensity peripheral electrical nerve stimulation did not have acute effects on healthy adults’ visuomotor performance but SES had delayed effects in the form of enhanced motor memory consolidation that were not scaled by the duration of SES