Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm

Berland, Julien; Bogey, Christophe; Bailly, Christophe

doi:10.1016/j.compfluid.2005.04.003

Cited by 195 publications

(133 citation statements)

References 9 publications

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“…Time integration is performed using a fourth-order, six-stage Runge-Kutta scheme, which has low dispersion and dissipation errors [13].…”

Section: Time Integrationmentioning

confidence: 99%

Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

Arina¹

2016

Aerospace

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Abstract:The propagation of small perturbations in complex geometries can involve hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes. A propagation model, based on the linearized Navier-Stokes equations, is proposed. It includes the mechanism responsible for the generation of vorticity associated with the hydrodynamic modes. The linearized Navier-Stokes equations are discretized in space using a discontinuous Galerkin formulation for unstructured grids. Explicit time integration and non-reflecting boundary conditions are described. The linearized Navier-Stokes (LNS) model is applied to two test cases. The first one is the time-harmonic source line in an incompressible inviscid two-dimensional mean shear flow in an infinite domain. It is shown that the proposed model is able to capture the trailing vorticity field developing behind the mass source and to represent the redistribution of the vorticity. The second test case deals with the analysis of the acoustic propagation of an incoming perturbation inside a circular duct with a sudden area expansion in the presence of a mean flow and the evaluation of its scattering matrix. The computed coefficients of the scattering matrix are compared to experimental data for three different Mach numbers of the mean flow, M 0 = 0.08, 0.19 and 0.29. The good agreement with the experimental data shows that the proposed method is suitable for characterizing the acoustic behavior of this kind of network.

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“…Time integration is performed using a fourth-order, six-stage Runge-Kutta scheme, which has low dispersion and dissipation errors [13].…”

Section: Time Integrationmentioning

confidence: 99%

Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

Arina¹

2016

Aerospace

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“…In the circumferential direction, a Fourier pseudo-spectral method is used to calculate the spatial derivatives. A fourth-order Runge-Kutta scheme [33] is employed for time integration. The numerical code has been validated extensively in previous investigations [18,34,25,22,24].…”

Section: Numerical Frameworkmentioning

confidence: 99%

Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

Luginsland

Gallaire

Kleiser

2016

European Journal of Mechanics - B/Fluids

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a b s t r a c tVortex breakdown of swirling, round jet flows is investigated in the compressible, subsonic regime by means of Direct Numerical Simulation (DNS). This is achieved by solving the compressible Navier-Stokes equations on a cylindrical grid using high-order spatial and temporal discretization schemes. TheReynolds number is Re = ρ The integral swirl number at the inflow is S int = 0.85. The parameters are chosen properly so as to make comparisons with existing experiments at lower Mach numbers possible while still enabling a study of compressible and baroclinic effects. Different from previous numerical investigations, a nozzle immersed in the fluid is included in the computational domain and is modelled as an isothermal no-slip wall, either rotating with the mean azimuthal flow direction or kept at rest. The present investigation aims to clarify the role played by the nozzle wall motion for the vortex breakdown of the swirling jet. We study the nozzle flow as well as the swirling jet flow simultaneously, a novelty for numerical investigations of vortex breakdown in swirling jets. Depending on the nozzle wall motion, the flow differs significantly upstream of the vortex breakdown: for the rotating nozzle, the flow inside the nozzle is purely laminar and the azimuthal boundary layer at the outer nozzle wall gives rise to the axisymmetric mode n = 0 and a single-helix type instability with azimuthal wave number n = 1. With the nozzle at rest, a transitional flow is observed within the nozzle where a helical instability with azimuthal wave number n = 12 dominates, growing in the boundary layer at the nozzle wall. For both nozzle setups, the helical instabilities observed for the nozzle flow interact with the developing vortex breakdown and the conical shear-layer downstream of the nozzle. For the nozzle at rest, this interaction results in a vortex breakdown configuration which is shifted in the upstream direction and which has a smaller radial and streamwise extent compared to the rotating nozzle case and the recirculation intensity is higher. The dominant frequency is highly influenced by the flow upstream of the vortex breakdown and is substantially higher for the nozzle at rest. Although the nozzle flow field differs for the two configurations and therefore alters the vortex breakdown downstream, a single-helix type instability n = 1 governing the vortex breakdown is found for both cases. This provides strong evidence for the robustness of the instability mechanisms leading to vortex breakdown.

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“…2. This magnetic field solution is used to integrate ions trajectories solving the Lorentz equation by means of modified fourth order Runge-Kutta algorithm 16 . The time-step is typically taken equal to 1/20 of the gyro-period at the particle current position which ensures energy conservation within 1% over the total integration duration.…”

Section: Non Axi-symmetry Effectsmentioning

confidence: 99%

Particle deconfinement in a bent magnetic mirror

Gueroult

Fisch

2012

Physics of Plasmas

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Coils misalignment in a magnetic mirror can produce additional particle transport.The magnetic field non axi-symmetry is responsible for radial and longitudinal drifts in a way much similar to the neo-classical transport in a tandem mirror cell distorted by end plugs. Accordingly, a regime exhibiting large radial displacements -similar to the resonant regime in tandem mirrors -can be obtained by confining ions azimuthally, for example by means of a properly tuned radial electric field. Because of the mass dependence of the magnetic field non-homogeneity drift velocities, the azimuthal trapping is mass specific, allowing in principle the filtering of a specific species based on its mass.1

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Low-dissipation and low-dispersion fourth-order Runge–Kutta algorithm

Cited by 195 publications

References 9 publications

Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

Particle deconfinement in a bent magnetic mirror

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