Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated. In particular, the advantages of using non-matching grids are presented, when one subregion has to be resolved by a substantially finer grid than the other subregion. We present the non-matching grid technique for the case of a mechanical-acoustic coupled as well as for acoustic-acoustic coupled systems. For the first case, the problem formulation remains essentially the same as for the matching situation, while for the acoustic-acoustic coupling, the formulation is enhanced with Lagrange multipliers within the framework of Mortar Finite Element Methods. The applications will clearly demonstrate the superiority of the Mortar Finite Element Method over the standard Finite Element Method both concerning the flexibility for the mesh generation as well as the computational time.

Standard compact scheme and upwinding compact scheme have high order accuracy and high resolution, but cannot capture the shock which is a discontinuity. This work developed a modified upwinding compact scheme which uses an effective shock detector to block compact scheme to cross the shock and a control function to mix the flux with WENO scheme near the shock. The new scheme makes the original compact scheme able to capture the shock sharply and, more importantly, keep high order accuracy and high resolution in the smooth area which is particularly important for shock boundary layer and shock acoustic interactions. Numerical results show the scheme is successful for 2-D Euler and 2-D Navier-Stokes solvers. The examples include 2-D incident shock, 2-D incident shock and boundary layer interaction. The scheme is robust, which does not involve case related parameters.

A localized flexible airfoil at low Reynolds numbers is modeled and the aerodynamic performance is analyzed numerically. With characteristic based split scheme, a fluid solver for two dimensional incompressible Navier-Stokes equations is developed under the ALE framework, coupled with the theory of shallow arch, which is approximated by Galerkin method. Further, the interactions between the unsteady flow and the shallow arch are studied in detail. In particular, the effect of the self-excited vibration of the structure on aerodynamic performance of the airfoil is investigated deeply at various angles of attack. The results show that the lift-to-drag ratio has been increased greatly compared with the rigid airfoil. Finally, the relationship between the self-excited vibration and the evolution of the flow is analyzed using FFT tools.

Our aim is to evidence new 3D composite diffractive structures whose effective permittivity tensor can exhibit very large positive or negative real eigenvalues. We use a reiterated homogenization procedure in which the first step consists in considering a bounded obstacle made of periodically disposed parallel high conducting metallic fibers of finite length and very thin cross section. As shown in [2], the resulting constitutive law is non-local. Then by reproducing periodically the same kind of obstacle at small scale, we obtain a local effective law described by a permittivity tensor that we make explicit as a function of the frequency. Due to internal resonances, the eigenvalues of this tensor have real part that change of sign and are possibly very large within some range of frequencies. Numerical simulations are shown.

Particle dynamics in a turbulent channel flow is considered. The effects of particle concentration and Reynolds number on the particle velocity statistics are investigated. Four different particle response times, τ+=1, 5, 30 and 100, are examined for three different Reynolds numbers, Re*=200, 360 and 790 (based on channel height and friction velocity). The particle concentration evolves with time and statistics obtained during three different sampling periods might be distinctly different. The mean and fluctuating particle velocities are substantially affected both by the particle response time and by the Reynolds number of the flow.

In this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.

The swimming of a 3D fish-like body with finlets is numerically investigated at Re = 1000 (the Reynolds number is based on the uniform upstream flow and the length of the fish-like body). The finlets are simply modeled as thin rigid rectangular plates that undulate with the body. The wake structures and the flow around the caudal peduncle are studied. The finlets redirect the local flow across the caudal peduncle but the vortical structures in the wake are almost not affected by the finlets. Improvement of hydrodynamic performance has not been found in the simulation based on this simple model. The present numerical result is in agreement with that of the work of Nauen and Lauder [J. Exp. Biol., 204 (2001), pp. 2251-2263] and partially supports the hypothesis of Webb [Bull. Fish. Res. Bd. Can., 190 (1975), pp. 1-159].

Propagation of light through curved graded index optical waveguides supporting an arbitrary high number of modes is investigated. The discussion is restricted to optical wave fields which are well confined within the core region and losses through radiation are neglected. Using coupled mode theory formalism, two new forms for the propagation kernel for the transverse electric (TE) wave as it travels along a curved two-dimensional waveguide are presented. One form, involving the notion of “bend” modes, is shown to be attractive from a computational point of view as it allows an efficient numerical evaluation of the optical field for sharply bent waveguides.

A new class of supersonic nonequilibrium flows is studied on the basis of solving the Boltzmann and model kinetic equations with the aim to consider new non-linear structures in open systems and to study anomalous transfer properties in relaxation zones. The Unified Flow Solver is applied for numerical simulations. Simple gases and gases with inner degrees of freedom are considered. The experimental data related to the influence of the so-called optical lattices on the supersonic molecular beams are considered and numerical analysis of the nonequilibrium states obtained on this basis is made. The nonuniform relaxation problem with these distributions is simulated numerically and anomalous transport is confirmed. The conditions for strong changes of the temperature in the anomalous transfer zones are discussed and are realized in computations.

Transparent boundary conditions (TBCs) for anisotropic vertical transverse isotropic VTI medium are formulated for the axially symmetric case. The high accuracy of the derived TBCs and their long-time stability are demonstrated in numerical experiments. The TBCs are represented in terms of the vertical component of the velocity vector and tangential component of the stress tensor that facilitates the easy implementation of the boundary condition into the finite-difference staggered-grid scheme.

We apply in this study an area preserving level set method to simulate gas/water interface flow. For the sake of accuracy, the spatial derivative terms in the equations of motion for an incompressible fluid flow are approximated by the fifth-order accurate upwinding combined compact difference (UCCD) scheme. This scheme development employs two coupled equations to calculate the first- and second-order derivative terms in the momentum equations. For accurately predicting the level set value, the interface tracking scheme is also developed to minimize phase error of the first-order derivative term shown in the pure advection equation. For the purpose of retaining the long-term accurate Hamiltonian in the advection equation for the level set function, the time derivative term is discretized by the sixth-order accurate symplectic Runge-Kutta scheme. Also, to keep as a distance function for ensuring the front having a finite thickness for all time, the re-initialization equation is used. For the verification of the optimized UCCD scheme for the pure advection equation, two benchmark problems have been chosen to investigate in this study. The level set method with excellent area conservation property proposed for capturing the interface in incompressible fluid flows is also verified by solving the dam-break, Rayleigh-Taylor instability, two-bubble rising in water, and droplet falling problems.

In the present work adaptation in meshless framework is proposed. The grid adaptation or mesh adaptation is quite well developed area in case of conventional grid based solvers and is popularly known as Adaptive mesh refinement (AMR). In such cases the adaptation is done by subdividing the cells or elements into finer cells or elements. In case of meshless methods there are no cells or elements but only a cloud of points. In this work we propose to achieve the meshless adaptation by locally refining the point density in the regions demanding higher resolution. This results into an adaptive enriched cloud of points. We call this method as Adaptive Cloud Refinement (ACR). The meshless solvers need connectivity information, which is a set of neighboring nodes. It is crucial part of meshless solvers. Obviously because of refining point density, the connectivity of nodes in such regions gets modified and hence has to be updated. An efficient connectivity update must exploit the fact that the node distribution would be largely unaffected except the region of adaptation. Hence connectivity updating needs to be done locally, only in these regions. In this paper we also present an extremely fast algorithm to update connectivity over adapted cloud called as ACU (Automatic Connectivity Update).

For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

Numerical simulations using CLSVOF (coupled level set and volume of fluid) method are performed to investigate the coalescence and splashing regimes when a spherical water drop hits on the water surface with an impingement angle. Impingement angle is the angle between the velocity vector of primary drop and the normal vector to water surface. The effect of impingement angle, impact velocity and the height of target liquid are carried out. The impingement angle is varied from 0° to 90° showing the gradual change in phenomena. The formation of ship pro like shape, liquid sheet, secondary drops and crater are seen. Crater height, crater displacement, crown height and crown angle are calculated and the change in the parameters with change in impingement angle is noted.

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.

The Boltzmann equation (BE) for gas flows is a time-dependent nonlinear differential-integral equation in 6 dimensions. The current simplified practice is to linearize the collision integral in BE by the BGK model using Maxwellian equilibrium distribution and to approximate the moment integrals by the discrete ordinate method (DOM) using a finite set of velocity quadrature points. Such simplification reduces the dimensions from 6 to 3, and leads to a set of linearized discrete BEs. The main difficulty of the currently used (conventional) numerical procedures occurs when the mean velocity and the variation of temperature are large that requires an extremely large number of quadrature points. In this paper, a novel dynamic scheme that requires only a small number of quadrature points is proposed. This is achieved by a velocity-coordinate transformation consisting of Galilean translation and thermal normalization so that the transformed velocity space is independent of mean velocity and temperature. This enables the efficient implementation of Gaussian-Hermite quadrature. The velocity quadrature points in the new velocity space are fixed while the correspondent quadrature points in the physical space change from time to time and from position to position. By this dynamic nature in the physical space, this new quadrature scheme is termed as the dynamic quadrature scheme (DQS). The DQS was implemented to the DOM and the lattice Boltzmann method (LBM). These new methods with DQS are therefore termed as the dynamic discrete ordinate method (DDOM) and the dynamic lattice Boltzmann method (DLBM), respectively. The new DDOM and DLBM have been tested and validated with several testing problems. Of the same accuracy in numerical results, the proposed schemes are much faster than the conventional schemes. Furthermore, the new DLBM have effectively removed the incompressible and isothermal restrictions encountered by the conventional LBM.

Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

We extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If X= (x1,x2,x3)ϵℝ3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region ∣x3∣ > ∣∣x∣γ, for γϵ(1/4,1/2) and x large. For ∣x3∣ < ∣∣x∣∣γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

We propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms. We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.