Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Stability analysis of lattice Boltzmann methods
Journal of Computational Physics
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Short Note: Error dynamics: Beyond von Neumann analysis
Journal of Computational Physics
Lattice Boltzmann method with selective viscosity filter
Journal of Computational Physics
Lattice Boltzmann method with selective viscosity filter
Journal of Computational Physics
Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics
Journal of Computational Physics
Application of Lattice Boltzmann Method to sensitivity analysis via complex differentiation
Journal of Computational Physics
A time-reversal lattice Boltzmann method
Journal of Computational Physics
Journal of Computational Physics
A lattice Boltzmann method for nonlinear disturbances around an arbitrary base flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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Computational aeroacoustic (CAA) simulation requires accurate schemes to capture the dynamics of acoustic fluctuations, which are weak compared with aerodynamic ones. In this paper, two kinds of schemes are studied and compared: the classical approach based on high order schemes for Navier-Stokes-like equations and the lattice Boltzmann method. The reference macroscopic equations are the 3D isothermal and compressible Navier-Stokes equations. A Von Neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions. Three physical modes are recovered and the corresponding theoretical dispersion relations are obtained. Then the same analysis is made on the space and time discretization of the Navier-Stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions. Different orders of discretization are considered, with and without a uniform mean flow. Three different lattice Boltzmann models are then presented and studied with the Von Neumann analysis. The theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied. It is shown that the dispersion error in the lattice Boltzmann models is only due to the space and time discretization and that the continuous discrete velocity Boltzmann equation yield the same exact dispersion as the Navier-Stokes equations. Finally, dispersion and dissipation errors of the different kind of schemes are quantitatively compared. It is found that the lattice Boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3-step Runge-Kutta scheme in time. The number of floating point operations at a given error level associated with these two kinds of schemes are then compared.