Prandtl-Meyer flow tables for parahydrogen at total temperatures from 30K to 290K and for nitrogen at total temperatures from 100K to 300K at total pressures from 1 ATM to 10 ATM

The dependency of Mach number on the Prandtl-Meyer function was numerically determined by iterating the Prandtl-Meyer function and applying the Muller method to converge on the Mach number for flows in cryogenic parahydrogen and nitrogen at various total pressures and total temperatures. The results are compared with the ideal diatomic gas values and are presented in tabular form

Tables of isentropic expansions of parahydrogen and related transport properties for total temperatures from 25 K to 300 K and for total pressures from 1 ATM to 10 ATM

The isentropic expansions of parahydrogen at various total pressures and total temperatures were numerically determined by iterating Mach number and by using a modified interval halving method. The calculated isentropic values and related properties are presented in tabulated form

A multirate approach for time domain simulation of very large power systems

The time evolution of power systems is modeled by systems of differential and algebraic equations (DAEs) [8]. The variables involved in these DAEs may exhibit different time scales. Some of the variables can be highly active while other variables can stay constant during the entire time integration period. In standard numerical time integration methods for DAEs the most active variables impose the time step for the whole system. We present a strategy, which allows the use of different, local time steps over the variables. The partitioning of the components of the system in different classes of activity is performed automatically based on the topology of the power system. The performance of the multirate approach for two case studies is presented

Absorption of spherical bubbles in a square microchannel

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Microfluidics is a fast growing field in which the manipulation of bubbles in liquid phase is of utmost importance. In this paper, the absorption of spherical bubbles in a square microchannel is investigated for a bubbly flow. Numerical simulations of the gas-liquid two-phase flow and the mass transfer around spherical bubbles in a square microchannel are carried out. Correlations are established for the bubble velocity and the mass transfer rate. A model for the dissolution of spherical bubbles along a square microchannel is proposed in the case of the bubbly flow regime and validated using existing experimental data. This model can be used, for instance, for designing microabsorbers for lab-on-a-chip applications

Parareal Convergence for Oscillatory PDEs with Finite Time-scale Separation

This is the final version. Available on open access from the Society for Industrial and Applied Mathematics via the DOI in this recordA variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse solver features a coordinate transformation and a fast-wave averag- ing method inspired by analysis of multiple scales PDEs and is integrated using an HMM-type method. However, for many physical applications the timescale separation is finite, not infinite. In this paper we prove con- vergence for finite timescale separaration by extending the error bound on the coarse propagator to this case. We show that convergence requires the solution of an optimization problem that involves the averaging win- dow interval, the time step, and the parameters in the problem. We also propose a method for choosing the averaging window relative to the time step based as a function of the finite frequencies inherent in the problem.University of Exete

The effect of two distinct fast time scales in the rotating, stratified Boussinesq equations: variations from quasi-geostrophy

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Inspired by the use of fast singular limits in time-parallel numerical methods for a single fast frequency, we consider the limiting, nonlinear dynamics for a system of partial differential equations when two fast, distinct time scales are present. First order slow equations are derived via the method of multiple time scales when the two small parameters are related by a rational power. We find that the resultant system depends only on the relationship of the two fast time-scales, i.e. which fast time is fastest? Using the theory of cancellation of fast oscillations, we show that with the appropriate assumptions on the nonlinear operator of the full system, this reduced slow system is exactly that which the solution will converge to if each asymptotic limit is considered sequentially. The same result is also obtained via the method of renormalization. The specific example of the rotating, stratified Boussinesq equations is explored in detail, indicating that the most common distinguished limit of this system – quasi-geostrophy, is not the only limiting asymptotic system.We wish to thank the 2 anonymous referees whose comments significantly enhanced the presentation and scope of this article. J. P. W. would like to thank A.Larios, K. Julien, G. Chini, and A. Farhat for various discussions that prompted and motivated this work as well as generous support from the Mathematics Department of Brigham Young University. All of the authors wish to acknowledge the DOE LANL/LDRD program for support, as well as the hospitality of the Courant Institute of New York University where some of this work was completed. Wingate also wishes to thank the University of Exeter for support during the completion of this manuscript

Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this record.This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory PDEs, which is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale performance for weather prediction is that the strong scaling limit – the parallel performance for a fixed problem size with an increasing number of processors – saturates. A main avenue to circumvent this problem is to introduce new numerical techniques that take advantage of time parallelism. In this paper we use a time-parallel approximation that retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original problem into a large set of independent terms and (b) solving each of these terms independently of each other which can now be accomplished on a large number of HPC resources. Our results are conducted on up to 3586 cores for problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions in the time-to-solution of 118.3 for spectral methods and 1503.0 for finite-difference methods with the parallelizationin-time approach. A developed and calibrated performance model gives the scalability limitations a-priory for this new approach and allows us to extrapolate the performance method towards large-scale system. This work has the potential to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied areas modelling oscillatory dominated problems.The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz. de). We also acknowledge use of Hartree Centre resources in this work on which the early evaluation of the parallelization concepts were done