Discrete flow mapping: transport of phase space densities on triangulated surfaces

Energy distributions of high-frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in molecular dynamics simulations. Solutions to these flow equations are often large-scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping , for solving such problems on triangulated surfaces. An application in structural dynamics, determining the vibroacoustic response of a cast aluminium car body component, is presented.

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Improved Approximation of Phase-Space Densities on Triangulated Domains Using Discrete Flow Mapping with p-Refinement

Journal of Scientific Computing ◽

10.1007/s10915-017-0397-8 ◽

2017 ◽

Vol 72 (3) ◽

pp. 1290-1312 ◽

Cited By ~ 6

Author(s):

Janis Bajars ◽

David J. Chappell ◽

Timo Hartmann ◽

Gregor Tanner

Keyword(s):

Phase Space ◽

Flow Mapping ◽

Discrete Flow

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Transport of phase space densities through tetrahedral meshes using discrete flow mapping

Journal of Computational Physics ◽

10.1016/j.jcp.2016.10.019 ◽

2017 ◽

Vol 328 ◽

pp. 95-108 ◽

Cited By ~ 5

Author(s):

Janis Bajars ◽

David J. Chappell ◽

Niels Søndergaard ◽

Gregor Tanner

Keyword(s):

Phase Space ◽

Flow Mapping ◽

Tetrahedral Meshes ◽

Discrete Flow

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Heat Transfer in Rotating Serpentine Passages With Trips Normal to the Flow

Journal of Turbomachinery ◽

10.1115/1.2928038 ◽

1992 ◽

Vol 114 (4) ◽

pp. 847-857 ◽

Cited By ~ 124

Author(s):

J. H. Wagner ◽

B. V. Johnson ◽

R. A. Graziani ◽

F. C. Yeh

Keyword(s):

Heat Transfer ◽

Turbine Blade ◽

Large Scale ◽

Flow Direction ◽

Operating Conditions ◽

Transfer Model ◽

Transfer Coefficients ◽

Flow Equations ◽

Turbine Blade Cooling ◽

Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat transfer increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.

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A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽

10.3390/fluids6040148 ◽

2021 ◽

Vol 6 (4) ◽

pp. 148

Author(s):

Seyed Amin Nabavizadeh ◽

Himel Barua ◽

Mohsen Eshraghi ◽

Sergio D. Felicelli

Keyword(s):

Natural Convection ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Large Scale ◽

Bgk Model ◽

Flow Equations ◽

Wide Range ◽

Prandtl Numbers ◽

Boltzmann Method ◽

Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

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Large-scale Structure and Turbulence Transport in the Young Solar Wind – Comparison of Parker Solar Probe Observations with a Global 3D Reynolds-averaged MHD Model

10.5194/egusphere-egu21-12726 ◽

2021 ◽

Author(s):

Rohit Chhiber ◽

Arcadi Usmanov ◽

William Matthaeus ◽

Melvyn Goldstein ◽

Riddhi Bandyopadhyay

Keyword(s):

Solar Wind ◽

Large Scale ◽

Transport Equations ◽

Turbulence Energy ◽

Reynolds Stresses ◽

Mean Flow ◽

Coulomb Collisions ◽

Flow Equations ◽

Simulation Results ◽

Turbulence Transport

<div>Simulation results from a global magnetohydrodynamic model of the solar corona and the solar wind are compared with Parker Solar Probe's (PSP) observations during its first several orbits. The fully three-dimensional model (Usmanov et al., 2018, ApJ, 865, 25) is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model accounts for effects of electron heat conduction, Coulomb collisions, Reynolds stresses, and heating of protons and electrons via nonlinear turbulent cascade. Turbulence transport equations for turbulence energy, cross helicity, and correlation length are solved concurrently with the mean-flow equations. We specify boundary conditions at the coronal base using solar synoptic magnetograms and calculate plasma, magnetic field, and turbulence parameters along the PSP trajectory. We also accumulate data from all orbits considered, to obtain the trends observed as a function of heliocentric distance. Comparison of simulation results with PSP data show general agreement. Finally, we generate synthetic fluctuations constrained by the local rms turbulence amplitude given by the model, and compare properties of this synthetic turbulence with PSP observations.</div>

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Advanced design of large scale microwave devices for space applications using space mapping optimization

2017 IEEE MTT-S International Microwave Symposium (IMS) ◽

10.1109/mwsym.2017.8058914 ◽

2017 ◽

Cited By ~ 3

Author(s):

M. A. Ismail ◽

Ming Yu

Keyword(s):

Large Scale ◽

Space Mapping ◽

Microwave Devices ◽

Space Applications

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A Scale-Selective Data Assimilation Approach to Improving Tropical Cyclone Track and Intensity Forecasts in a Limited-Area Model: A Case Study of Hurricane Felix (2007)

Weather and Forecasting ◽

10.1175/waf-d-10-05033.1 ◽

2012 ◽

Vol 27 (1) ◽

pp. 124-140 ◽

Cited By ~ 11

Author(s):

Bin Liu ◽

Lian Xie

Keyword(s):

Data Assimilation ◽

Large Scale ◽

Dynamical Downscaling ◽

Weather Forecasting ◽

Forecast Error ◽

Regional Model ◽

Small Scale ◽

Limited Area ◽

Track Forecast ◽

Global Models

Abstract Accurately forecasting a tropical cyclone’s (TC) track and intensity remains one of the top priorities in weather forecasting. A dynamical downscaling approach based on the scale-selective data assimilation (SSDA) method is applied to demonstrate its effectiveness in TC track and intensity forecasting. The SSDA approach retains the merits of global models in representing large-scale environmental flows and regional models in describing small-scale characteristics. The regional model is driven from the model domain interior by assimilating large-scale flows from global models, as well as from the model lateral boundaries by the conventional sponge zone relaxation. By using Hurricane Felix (2007) as a demonstration case, it is shown that, by assimilating large-scale flows from the Global Forecast System (GFS) forecasts into the regional model, the SSDA experiments perform better than both the original GFS forecasts and the control experiments, in which the regional model is only driven by lateral boundary conditions. The overall mean track forecast error for the SSDA experiments is reduced by over 40% relative to the control experiments, and by about 30% relative to the GFS forecasts, respectively. In terms of TC intensity, benefiting from higher grid resolution that better represents regional and small-scale processes, both the control and SSDA runs outperform the GFS forecasts. The SSDA runs show approximately 14% less overall mean intensity forecast error than do the control runs. It should be noted that, for the Felix case, the advantage of SSDA becomes more evident for forecasts with a lead time longer than 48 h.

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Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.534 ◽

2019 ◽

Vol 875 ◽

pp. 1145-1174 ◽

Cited By ~ 6

Author(s):

T. Congy ◽

G. A. El ◽

M. A. Hoefer

Keyword(s):

Water Waves ◽

Large Scale ◽

Kdv Equation ◽

Linear Wave ◽

Mean Flow ◽

Undular Bore ◽

Expansion Waves ◽

Flow Interaction ◽

The Kdv Equation ◽

New Type

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

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