Artificial Selective Damping Research Articles

A nodal discontinuous Galerkin method for computational aeroacoustics and comparison with finite difference schemes

A nodal discontinuous Galerkin formulation, which is based on Lagrange polynomials basis, is used to directly simulate the acoustic wave propagation. Two test problems of wave propagation with initial disturbance consisting of a Gaussian profile or rectangular pulse are investigated. We evaluate the performance of the schemes in short, intermediate, and long waves. Moreover, the comparisons of numerical results between the nodal discontinuous Galerkin method and finite difference type schemes are performed, which indicate that the numerical solution obtained using nodal discontinuous Galerkin method with a pure central flux has obvious high frequency oscillations for initial disturbance consisting of rectangular pulse, which is the same as those obtained using finite difference type schemes without artificial selective damping. If an upwind flux is adopted, spurious waves are eliminated effectively except for the location of discontinuities. When a limiter is used, obviously the spurious short waves are almost completely removed. The quality of the computed solution has greatly improved.

Large Eddy Simulation of Supersonic Jet Noise from a Circular Nozzle

An imperfectly expanded supersonic jet is simulated with large eddy simulation (LES) method. The full 3D filtered Navier-Stokes equations in cylindrical coordinates coupled with the standard Smagorinsky model are solved by a computational aeroacoustic method. The Dispersion-Relation-Preserving scheme is used for spatial discretization and the low dissipation low dispersion Runge-Kutta method in 2N storage form is utilized for time marching. A high order explicit spatial filter is applied to remove the grid oscillations. An adaptive artificial selective damping is used for shock capturing. The supersonic jet with Mach number 1.19 is simulated. The simultaneous and time average flow field is analyzed. The near filed noise spectra are presented and compared with the experimental data of Ponton et al. and with the numerical results of the present authors by unsteady Reynolds averaged Navier-Stokes (URANS) method. It is shown that the numerical results by LES method agree better with the experimental data than the results by URANS method.

Recent advances in computational aeroacoustics

There are intrinsic differences between the characteristics and the objectives of aeroacoustics problems and typical fluid dynamics problems. These differences are not addressed by computational fluid dynamics (CFD). They form some of the major challenges to computational aeroacoustics (CAA). Recent advances in CAA methodologies to meet those challenges are reviewed. They include the development of high resolution CAA methods, artificial selective damping and high quality numerical boundary conditions. One unique development in CAA that has no counterpart in CFD is the wave number analysis approach. Wave number analysis not only can yield an absolute error incurred in the use of a discretized computational method but also offers a way to develop optimized computation schemes. It is indispensable in analyzing dispersion and dissipation errors associated with wave propagation computations. To illustrate the impact of CAA on aeroacoustics, an example of CAA application will be briefly discussed. As CAA application expands in scope, new challenges to CAA emerge. Some of the more pressing challenges that may well chart the future development of CAA methodology are elaborated.

Finite Volume Formulation of Compact Upwind and Central Schemes with Artificial Selective Damping

The present paper describes the use of compact upwind and compact central schemes in a Finite Volume formulation with an extension towards arbitrary meshes. The different schemes are analyzed and tested on several numerical experiments. A new formulation of artificial selective damping that is applicable on non-uniform Cartesian meshes is presented. Results are shown for a 1D advection equation, a 2D rotating Gaussian pulse and a subsonic inviscid vortical flow on uniform and non-uniform meshes and for a non-linear acoustic pulse.

Multi-size-mesh Multi-time-step Dispersion-relation-preserving Scheme for Multiple-scales Aeroacoustics Problems

The optimized high-order Dispersion-Relation-Preserving finite difference scheme is extended so as to be able to compute multiple-scales aeroacoustics problems effectively and efficiently. It is proposed that a multi-size-mesh is used in the computation. In implementing the time marching scheme, the computation domain is first partitioned into a number of subdomains. In each subdomain, a single size mesh is used. The mesh size of adjacent subdomain changes by a factor of two. The time step of adjacent subdomains also changes by the same ratio. This choice serves not only to maintain numerical stability but also to avoid unnecessary computations in regions with large size mesh. To pass information between subdomains, special optimized stencils are used at the subdomain interface region. Because rapid changes take place at the mesh-size-change interfaces, they are likely sources of spurious numerical waves. To prevent the generation and spreading of spurious numerical waves, special artificial selective damping terms are developed for inclusion in the discretized scheme. As an illustration of the efficacy of the multi-size-mesh multi-time-step scheme, it is applied to the simulation of an automobile door cavity tone problem. The computed tone frequencies are found to agree well with experimental measurements.

Perfectly Matched Layer as an Absorbing Boundary Condition for the Linearized Euler Equations in Open and Ducted Domains

Recently, perfectly matched layer (PML) as an absorbing boundary condition has found widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave modes are dispersive. It will be shown that in the presence of a mean flow the group velocity and phase velocity of these modes can have opposite signs. This results in a band of transmitted waves in the PML to be spatially amplifying instead of evanescent. Thus in a confined environment, PML may not be suitable as an absorbing boundary condition unless there is no mean flow.

A STUDY OF THE SHORT WAVE COMPONENTS IN COMPUTATIONAL ACOUSTICS

It is shown by using a Dispersion-Relation-Preserving [Formula: see text] finite difference scheme that it is feasible to perform direct numerical simulation of acoustic wave propagation problems. The finite difference equations of the [Formula: see text] scheme have essentially the same Fourier-Laplace transforms and hence dispersion relations as the original linearized Euler equations over a broad range of wavenumbers (here referred to as long waves). Thus it is guaranteed that the acoustic waves, the entropy and the vorticity waves computed by the [Formula: see text] scheme are good approximations of those of the exact solutions of Euler equations as long as the wavenumbers are in the long wave range. Computed waves with higher wavenumber, or the short waves, generally have totally different propagation characteristics. There are no counterparts of such waves in the exact solutions. The short waves of a computation scheme are, therefore, contaminants of the numerical solutions. The characteristics of these short waves are analyzed here by group velocity consideration and standard dispersive wave theory. Numerical results of direct simulations of these waves are reported. These waves can be generated by discontinuous initial conditions. To purge the short waves so as to improve the quality of the numerical solution, it is suggested that artificial selective damping terms be added to the finite difference scheme. It is shown how the coefficients of such damping terms may be chosen so that damping is confined primarily to the high wavenumber range. This is important for then only the short waves are damped leaving the long waves basically unaffected. The effectiveness of the artificial selective damping terms is demonstrated by direct numerical simulations involving acoustic wave pulses with discontinuous wave fronts.