Dynamical behavior of traveling wave solutions of ion acoustic plasma equations

By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-smooth periodic waves. Under the given parametric conditions, we present the sufficient conditions to guarantee the existence of the above solutions.

Theconvolutionaldiferentiatormethodfornu┐mericalmodelingofacousticandelasticwave┐fields

Based on the techniques of forward and inverse Fourier transformation, the authors discussed the design scheme of ordinary differentiator used and applied in the simulation of acoustic and elastic wavefields in isotropic media respectively. To compress Gibbs effects by truncation effectively, Hanning window is introduced in. The model computation shows that, the convolutional differentiator method has the advantages of rapidity, low requirements of computer′s inner storage and high precision, which is a potential method of numerical simulation.

Acoustic finite-difference modeling beyond conventional Courant-Friedrichs-Lewy stability limit:Approach based on variable-length temporal and spatial operators

Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectively,thereby limiting time step selection.Based on the definition of temporal and spatial FD operators,we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy.First,to simulate wave propagation beyond the conventional CFL stability limit,the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones.Second,to preserve the modeling accuracy,the velocity-dependent lengths of the temporal and spatial operators are adaptively varied.The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples,respectively.We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.

ACOUSTIC PROPAGATION IN SHEARED MEAN FLOW USING COMPUTATIONAL AEROACOUSTICS

Acoustic propagation problems in the sheared mean flow are numerically investigated using different acoustic propagation equations , including linearized Euler equations ( LEE ) and acoustic perturbation equations ( APE ) .The resulted acoustic pressure is compared for the cases of uniform mean flow and sheared mean flow using both APE and LEE.Numerical results show that interactions between acoustics and mean flow should be properly considered to better understand noise propagation problems , and the suitable option of the different acoustic equations is indicated by the present comparisons.Moreover , the ability of APE to predict acoustic propagation is validated.APE can replace LEE when the 3-D flow-induced noise problem is solved , thus computational cost can decrease.

PREDICTION OF ACOUSTIC PERFORMANCE IN EXPANSION CHAMBER MUFFLERS WITH MEAN FLOW BY FINITE ELEMENT METHOD

The equation of wave propagation in a circular chamber with mean flow is obtained. Computational solution based on finite element method is employed to determine the transmission loss of expansive chamber. The effect of the mean flow and geometry (length of expansion chamber and expansion ratio)on acoustic attenuation performance is discussed, the predicted values of transmission loss of expansion chamber without and with mean flow are compared with those reported in the literature and they agree well. The accuracy of the prediction of transmission loss implies that finite element approximations are applicable to a lot of practical applications.

Simulation of detection and scattering of sound waves by the lateral line of a fish

A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks,as well as the cross section of sound scattering on both the lines,strongly depends on angles of incidence of incoming sound waves.The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming.

On the application of wavelet transform to the solution of integral equations for acoustic radiation and scattering

The application of wavelets is explored to solve acoustic radiation and scattering problems. A new wavelet approach is presented for solving two-dimensional and axisymmetric acoustic problems. It is different from the previous methods in which Galerkin formulation or wavelet matrix transform approach is used. The boundary quantities are expended in terms of a basis of the periodic, orthogonal wavelets on the interval. Using wavelet transform leads a highly sparse matrix system. It can avoid an additional integration in Galerkin formulation, which may be very computationally expensive. The techniques of the singular integrals in two-dimensional and axisymmetric wavelet formulation are proposed. The new method can solve the boundary value problems with Dirichlet, Neumann and mixed conditions and treat axisymmetric bodies with arbitrary boundary conditions. It can be suitable for the solution at large wave numbers. A series of numerical examples are given. The comparisons of the results from new approach with those from boundary element method and analytical solutions demonstrate that the new techique has a fast convergence and high accuracy.

A Weak Galerkin Mixed Finite Element Method for AcousticWave Equation

This paper is concerned with the weak Galerkin mixed finite element method(WG-MFEM)for the second-order hyperbolic acoustic wave equation in velocity-pressure formulation.In this formulation,the original second-order differential equation in time and space is reduced to first-order differential equations by introducing the velocity and pressure variables.We employ the usual discontinuous piecewise-polynomials of degree k0 for the pressure and k+1 for the velocity.Furthermore,the normal component of the pressure on the interface of elements is enhanced by polynomials of degree k+1.The time derivative is approximated by the backward Euler difference.We show the stability of the semi-discrete and fullydiscrete schemes,and obtain the suboptimal order error estimates for the velocity and pressure variables.Numerical experiment confirms our theoretical analysis.

STABILITY FOR IMPOSING ABSORBING BOUNDARY CONDITIONS IN THE FINITE ELEMENT SIMULATION OF ACOUSTIC WAVE PROPAGATION＊

It is well-known that artificial boundary conditions are crucial for the efficient and accurate computations of wavefields on unbounded domains. In this paper, we investigate stability analysis for the wave equation coupled with the first and the second order absorbing boundary conditions. The computational scheme is also developed. The approach allows the absorbing boundary conditions to be naturally imposed, which makes it easier for us to construct high order schemes for the absorbing boundary conditions. A thirdorder Lagrange finite element method with mass lumping is applied to obtain the spatial discretization of the wave equation. The resulting scheme is stable and is very efficient since no matrix inversion is needed at each time step. Moreover, we have shown both abstract and explicit conditional stability results for the fully-discrete schemes. The results are helpful for designing computational parameters in computations. Numerical computations are illustrated to show the efficiency and accuracy of our method. In particular, essentially no boundary reflection is seen at the artificial boundaries.

High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation

We present a new high ordermethod in space and time for solving the wave equation,based on a newinterpretation of the“Modified Equation”technique.Indeed,contrary to most of the works,we consider the time discretization before the space discretization.After the time discretization,an additional biharmonic operator appears,which can not be discretized by classical finite elements.We propose a new Discontinuous Galerkinmethod for the discretization of this operator,andwe provide numerical experiments proving that the new method is more accurate than the classicalModified Equation technique with a lower computational burden.

Efficient Simulation of Wave Propagation with Implicit Finite Difference Schemes

Finite difference method is an important methodology in the approximation of waves.In this paper,we will study two implicit finite difference schemes for the simulation of waves.They are the weighted alternating direction implicit(ADI)scheme and the locally one-dimensional(LOD)scheme.The approximation errors,stability conditions,and dispersion relations for both schemes are investigated.Our analysis shows that the LOD implicit scheme has less dispersion error than that of the ADI scheme.Moreover,the unconditional stability for both schemes with arbitrary spatial accuracy is established for the first time.In order to improve computational efficiency,numerical algorithms based on message passing interface(MPI)are implemented.Numerical examples of wave propagation in a three-layer model and a standard complex model are presented.Our analysis and comparisons show that both ADI and LOD schemes are able to efficiently and accurately simulate wave propagation in complex media.