Top PDF Properties of highly nonlinear waves in compressible flows

Properties of highly nonlinear waves in compressible flows

Properties of highly nonlinear waves in compressible flows

Having investigated a possible scenario for wave generation in the lower atmosphere, I decided to examine in detail the process by which wave energy can be lost from a propagating highly[r]

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Near-wall scaling for incompressible and compressible flows

Near-wall scaling for incompressible and compressible flows

Comparisons between simulation S2 (WM) and S3 (WM-DPDX) are shown in Figure 29 and Figure 30 for the streamwise velocity component at two different positions in the flow. Figure 29 compares the mean streamwise velocity at x/h = 0.05 to the DNS data used for the a priori analysis. Simulation S2 with the simple wall model shows an overprediction of the velocity gradient. Including the pressure gradient formulation in our wall model simulation S3 improves the results. The average streamwise velocity profile follows the DNS data closely. A similar behaviour can be observed for the velocity profile at x/h = 8. This is a position close to the wall shear stress maximum (x/h ≈ 8.7). The wall model implementation with pressure gradient used in Simulation S3 is an improvement to Simulation S2. Most striking is the improvement of the gradient of the streamwise velocity at x/h = 0.05 close to the hill top. The wall model without pressure gradient is not able to capture the slope of the average profile. This confirms a priori investigations which have shown that velocity profiles at this position show much better agreement with the proposed scaling. In addition to that the improved slope of the velocity profile at x/h = 0.05 could be a result from the improved near-wall prediction at x/h = 8 ( Figure 30) since it influences the formation of the shear layer and as a result the flow properties at the hill top.
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On the implicit density based OpenFOAM solver for turbulent compressible flows

On the implicit density based OpenFOAM solver for turbulent compressible flows

The fully implicit coupled methods (see eg. [5], [3]) provides much better efficiency usually at the price of much higher complexity of the code and higher mem- ory requirements. Besides the fully implicit method the matrix-free LU-SGS (lower-upper symmetric Gauss-Seidel, [3]) method shares the appealing properties of fully im- plicit methods (i.e. the unconditional stability) with low code complexity and low memory overhead. In their re- cent paper [15] Shen at al. give detailed description of the implementation of LU-SGS method in the frame- work of OpenFOAM for the case of inviscid compressible flows. We follow their work and extend the LU-SGS based solver to turbulent flows described by the set of Reynolds- averaged Navier–Stokes equations combined with an ad- ditional turbulence model provided by the OpenFOAM package.
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A Jacobian-free edged-based Galerkin formulation for compressible flows

A Jacobian-free edged-based Galerkin formulation for compressible flows

The effectiveness of Krylov subspace linear system solvers depends on good preconditioners. The widely-used Incomplete Lower-Upper (ILU) factorization not only requires storing the system matrix but also its factorization, thus doubling the memory footprint. To the best of the authors’ knowledge, three alternate options are available. The first one is the Jacobi preconditioner, which can be implemented in a Jacobian-free fashion. This method only requires the diagonal of the Jacobian. While it seems numerically advantageous, a large number of linear iterations might be required for convergence. The second alternative is the multiplicative-additive Schwarz preconditioned inexact Newton [9] approach, which is a nonlinear Jacobian-free preconditioning method designed to overcome unbalanced nonlinearities coming from different ranges of time and spatial scales, such as shock waves and reaction fronts, but only two-dimensional incompressible flow test cases have been presented in the reference. The last alternative, adopted in this work, is LU-SGS [4]. It was originally developed as a solver for inviscid flows on structured grids, but has recently been extended to viscous flows and unstructured meshes [10] [11]. In LU-SGS, the implicit operator is simplified by introducing a Roe-type flux approximation that replaces the Roe matrix with its spectral radius, consequently only the diagonal part of the Jacobian is stored and the products of the off-diagonal terms and the solution update are approximated by a Fréchet derivative through a forward and a backward sweep. However, in the original LU-SGS, the viscous Jacobian is identified as a scalar in the spectral radius and the contributions from boundary conditions are omitted. In this work, the viscous Jacobian is taken into account by computing it on the fly during the two sweeps. Riemann, supersonic outlet, slip wall and non-slip wall boundary conditions are included in the computation of the Jacobian.
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Comparison of high order algorithms in Aerosol and Aghora for compressible flows

Comparison of high order algorithms in Aerosol and Aghora for compressible flows

Aerosol is a high order finite element library based on both continuous and discontinuous elements on hybrid meshes involving triangles and quadrangles in two dimensions and tetrahedra, hexahedra and prisms in three dimensions. More precisely, the finite element classes are generated up to the fourth order polynomial approximation. Currently, it is possible to solve simple problems with the continuous Galerkin method (Laplace equation, SUPG stabilized advection equations), with the discontinous Galerkin method (first order hyperbolic systems) and with residual distribution schemes (scalar hyperbolic equations). It is written in C++ , and its development started nearly from scratch as far as the general structure of the code is concerned. It strongly depends on the PaMPA library for memory handling, for mesh partitioning, and for abstracting the MPI layer (see next section for details). It is linked with external linear solvers (up to now, PETSc 4 and MUMPS 5 ). It is about to use the StarPU 6 task scheduler for hybrid architectures. StarPU is also being developed at INRIA. The choice of C++ allows for a good flexibility in terms of models and equations of state. Currently, the following models can be used: scalar advection, waves in a first order formulation, nonlinear scalar hyperbolic equation and Euler model with an abstract equation of state (currently: perfect gas and stiffened gas equation of state). It works on linear elements, but the level of abstraction is sufficient for taking into account curved elements.
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Numerical Methods for Compressible Multi-phase flows with Surface Tension

Numerical Methods for Compressible Multi-phase flows with Surface Tension

and which has been successively applied to general nonlinear hyperbolic conservation laws and to non-conservative hyperbolic systems. The classical Osher-Solomon scheme is very complex and computationally expensive. Hence a new Osher solver is applied by using an appropriate Gaussian quadrature rule for computing path integrals that arise in the definition of the dissipative part of the Osher-Solomon flux. The DOT scheme has some general attractive advantages, such as computational robustness, entropy satisfaction, good behaviour for slowly-moving shocks and smoothness. A much simpler approach is that the local Lax-Friedrichs or the Rusanov method [129], which uses a one-wave model. Since the intermediate waves are not considered, the Rusanov Riemann solver contains the penalty of a high level of numerical dissipation. The Rusanov method is a so-called incomplete Riemann solver. In a very recent paper of Dumbser et al [61], a novel HLLEM Riemann solver has been extended to general conservative and non-conservative hyper- bolic systems. This method was first proposed by Einfeldt [67] and Einfeldt et al [69] with its applications to the compressible Euler equations. It assumes no longer a constant intermediate state, but a piecewise linear distribution. For other approximate Riemann solvers, the reader is referred to [148, 96].
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Non Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

Non Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

The dynamic properties of granular chains have been conventionally studied using dis- crete particle models (DPMs), which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although this is a good approximation under proper circumstances, it doesn’t capture many features of the three-dimensional elastic particles, such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes of the contact area, and the collective vibrations of the particles, among others. Therefore, the goal of this research is to develop a finite element model, using commercially available software Abaqus, which is capable of taking into account many of these characteristic features. The finite element model developed in this work will be able to discretize particles by considering them as three-dimensional deformable bodies of revolution. The model will also be helpful in understanding the interaction behavior between nonspherical particles, and its dependence on particles’ geometry and orientation. It will also be useful in studying the interface dynamics of granular chains and adjacent linear elastic media, which can be a viable and useful tool in the future to numerically study the NDE/SHM of complicated structures using granular chains as an actuator/sensing device.
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Modelling compressible multiphase flows

Modelling compressible multiphase flows

A second point is that these highly non-linear systems involve many different time scales that lie within a very wide range; a straightforward consequence is that high-order efficient and stable enough schemes are mandatory if one expects to get unsteady approximations that are not too far from mesh convergence. This urges the development of hybrid implicit-explicit schemes in order to obtain accurate approximations of components associated with slow internal waves. Relaxation schemes seem to provide a fair framework that might handle complex equations of state, and mean- while provide accurate enough approximations.
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Linear and Nonlinear Dynamics of Spin Waves in Ferromagnetic Nanowires

Linear and Nonlinear Dynamics of Spin Waves in Ferromagnetic Nanowires

Furthermore, in Chapters 2, 3, 5, 6 and 7 we presented a series of new results for the nonlinear instabilities (due to microwave pumping) of the SWs in NWs and ultrathin films. The previous work on the pumping of nonlinear dipole-exchange SWs had generally employed macroscopic theories. The smaller dimensions of the nanostructural NWs and films studied here are interesting because the spatial quantization of the eigenmodes become predominant and therefore our theory employs a microscopic method. Accordingly, our new results for the instability thresholds versus applied field (the butterfly curves) are significantly modified compared to those for macroscopic samples, and they show structural featured related to the discrete SW branches of the NWs. The SW properties for NWs and ultrathin films are also found to be quite di ff erent from one another, since they are characterized by 1D and 2D wave vectors, respectively. The material of Chapter 5 (which was published as a paper in Journal of Physics: Condensed Matter) was selected by the journal editors as a news highlight paper.
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Making Waves: Visualizing Fluid Flows

Making Waves: Visualizing Fluid Flows

Our wooden reliefs of wave breaking and our results on beach erosion by breaking waves led Pepijn Pinkse (personal communication, University of Twente) to point out to us that similar erosional features are found on much smaller scales. Ion-beam sputtering of Silicium or Germanium surfaces cause these surfaces to erode in beautiful patterns. These patterns cannot be observed directly, but only with the aid of atomic force microscopy (AFM). To render these patterns appreciable, Wout Zweers scaled up the images from Frost's scientific article [3] to make the laser engravings in Fig. 2.
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Existence of the weak solutions for the compressible magnetohydrodynamic flows driven by stochastic forcing

Existence of the weak solutions for the compressible magnetohydrodynamic flows driven by stochastic forcing

In this paper, we study the existence of weak solutions for the compressible magnetohydrodynamics flows driven by stochastic external forcing. Our method is based on solving the system for each fixed representative of the random variable and applying an abstract result on the measurability of multi-valued maps.

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Stability of Stratified Compressible Shear Flow

Stability of Stratified Compressible Shear Flow

In the present chapter we have studied the effect of a magnetic field on linear stability of stratified horizontal flows of an in viscid compressible fluid by the generalized progressing wave expansion method . Here we have discussed the different cases and have established the conditions for the stability. It is found that the magnetic field stabilizes the system.

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Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

The layered Eqs. (21)–(24) are solved with the non- oscillatory, shock-capturing method of Jiang and Tadmor (1998). A shock-capturing method was employed since these nonlinear, hydrostatic equations can be expected to lead to wave steepening and breaking. This numerical method is ad- vantageous since it naturally allows the numerical solutions to proceed smoothly when shocks form as demonstrated in the results below. We note that the equations above, while in a flux form suitable for shock capturing, do not preserve mo- mentum flux across a shock. Indeed, even the two-layered version of these equations do not possess this property. The fundamental issue concerns the distribution between the lay- ers of the energy loss across the shock. A discussion of this issue can be found in Klemp et al. (1997) for two-layer flows. Jiang and Smith (2001) highlight the role of viscosity in re- solving the problem. Since our focus is not on the shock dy- namics, we allow shocks to form, but restrict our analysis of the numerical results to shock-free regions where we search for simple-wave behavior. Note that if either non-hydrostatic effects or significant (turbulent) viscosity were included in the model the shocks would have a finite length or not form at all.
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A hybrid molecular-continuum method for unsteady compressible multiscale flows

A hybrid molecular-continuum method for unsteady compressible multiscale flows

Molecular dynamics (MD) is currently the best method available to simulate these types of flows accurately. The fluid and solid parts of the problem are modelled using molecular constituents (atoms and molecules), whose behaviour in space and time is described by Newton’s equations of motion and intermolecular potentials derived from quantum mechanics or experiment. The problem with MD, however, is that it is very computationally intensive. Current processing power prohibits a full molecular calculation of systems any larger than a few nanometres for a few nanoseconds of problem time. A hybrid molecular–continuum approach is therefore an attractive alternative: it aims to combine the best attributes of both MD (i.e. molecular detail) and a continuum-fluid formulation (i.e. computational cheapness).
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Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena

Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena

These relaxation phenomena assume infinitely fast mass, momentum and energy transfers between phases. Yet these transfers obey their own associated kinetics. For example in a multiphase medium the pressure equilibrium between phases is reached much faster than the thermal equilibrium. Indeed the pressure fluctuations are due to acoustic waves propagation inside the medium which is faster than heat diffusion. Thus the characteristic time scales of the various relaxation phenomena mentioned above may be strongly different. Some of the relaxation phenomena have been studied recently in [3, 7, 9, 19] for different configurations where phase change effects are present.
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Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows

Domain decomposition preconditioners for discontinuous Galerkin discretizations of compressible fluid flows

Despite the advantages and capabilities of the DGFEM, the method is not yet mature and current implementations are subject to strong limitations for its application to large scale industrial problems. This situation is clearly reflected by the breadth of research ac- tivity and the increasing number of scientific articles concerning DGFEMs. In particular, one of the key issues is the design of efficient strategies for the solution of the system of equations generated by a DGFEM, which we should point out is typically larger than the corresponding matrix system generated when a conforming finite element method is em- ployed. However, in the context of p–version finite element methods, it has been shown in the recent article [ 17 ] that DGFEMs can indeed outperform their conforming counterparts in the sense that the former class of methods may be more accurate for a given number of degrees of freedom as the polynomial degree is increased. For two–dimensional problems, parallel direct solvers such as MUMPS [ 1–3 ] , for example, are generally applicable. How- ever, for such problems, they still require very large amounts of memory in order to store the L and U factors. Moreover, for three-dimensional calculations, direct methods become impractical. Thereby, in this setting iterative solvers, such as GMRES, for example, must be exploited. Of course, the key to computing the solution in an efficient manner relies on the choice of the underlying preconditioning strategy employed. In order to exploit the parallel capabilities of modern high performance computing architectures, it is natural to consider multilevel techniques, which are based on exploiting some form of domain de- composition approach, such as additive and multiplicative Schwarz preconditioners, since they are naturally highly-parallelizable and scalable to a large number of processors.
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A note on regularity criterion for 3D compressible nematic liquid crystal flows

A note on regularity criterion for 3D compressible nematic liquid crystal flows

A note on regularity criterion for 3D compressible nematic liquid crystal flows Xiaochun Chen1* and Jishan Fan2 * Correspondence: xiaochunchen1@gmail.com 1 College of Mathematics and Sta[r]

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Nonlinear plasmonics in a two-dimensional plasma layer

Nonlinear plasmonics in a two-dimensional plasma layer

In conclusion, we have investigated the nonlinear behavior of plasmons in a 2D plasma layer. For a periodic large-amplitude wave, the harmonic generation leads to a nonlinear upshift of the frequency. The large amplitude wave-train is subject to a modulational instability that leads to the growth of sidebands and modulation of the periodic wavetrain. The linear dispersion of the 2D plasmons, as well as their nonlinear frequency upshift and modulational instability, have an interesting analogy in gravity waves such as ocean waves. Direct numerical simulations of the dynamical system con fi rm both the predicted nonlinear upshift of the frequency and the growth-rate of the modulational instability. The wavetrain eventually breaks up into a series of modulated pulses and more complicated wave turbulence. The spatial and temporal wave spectra show a dual cascade of wave energy to both higher and lower frequencies associated with components at both smaller and larger length-scales.
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Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

speed of sound at some reference state c specific heat of the part icle cloud c, specific he at of the p article cloud with radius specific heat of the particle cloud with radius specifi[r]

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A hybrid molecular–continuum method for unsteady compressible multiscale flows

A hybrid molecular–continuum method for unsteady compressible multiscale flows

molecular simulation. This is discussed in more detail in Borg, Lockerby & Reese (2013c), Patronis et al. (2013) and Patronis & Lockerby (2014). The internal-flow multiscale method (IMM) of Borg et al. (2013c) was developed instead for these kind of geometries, and for isothermal, incompressible, steady flows. The method consists of iteratively solving a one-dimensional (1D) steady continuity equation; MD simulations are applied at regularly spaced nodes along the streamwise direction of the domain, with heights chosen to match the local geometry of the full channel (see figure 1). Measurements of mass flow rates are extracted from these MD subdomains, which are then used to evaluate macro continuity errors. Based on these errors the equivalent pressure gradients (i.e. body forces) applied to each MD simulation are adjusted. A converged solution is obtained after only a few (typically two or three) iterations. As the fluid and wall conditions are defined from a microscopic (intermolecular) perspective in the micro elements, non-continuum models for slip, density layering, and non-local viscosity and stress are not required in the macro description. The flow rate is the sole parameter measured in the micro solutions, and provides an adequate and sufficient micro-to-macro coupling. However, several problems with this simple approach have become evident, in particular, the fluid compressibility is not incorporated and the method is only applicable to steady flows.
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