Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme

A weighted compact nonlinear scheme (WCNS) is applied to numerical simulations of compressible multicomponent flows, and four different implementations (fully or quasi-conservative forms and conservative or primitive variables interpolations) are examined in order to investigate numerical oscillation generated in each implementation. The results show that the different types of numerical oscillation in pressure field are generated when fully conservative form or interpolation of conservative variables is selected, while quasi-conservative form generally has poor mass conservation property. The WCNS implementation with quasi-conservative form and interpolation of primitive variables can suppress these oscillations similar to previous finite volume WENO scheme, despite the present scheme is finite difference formulation and computationally cheaper for multi-dimensional problems. Series of analysis conducted in this study show that the numerical oscillation due to fully conservative form is generated only in initial flow fields, while the numerical oscillation due to interpolation of conservative variables exists during the computations, which leads to significant spurious numerical oscillations near interfaces of different component of fluids. The error due to fully conservative form can be greatly reduced by smoothing interface, while the numerical oscillation due to interpolation of conservative variables cannot be significantly reduced. The primitive variable interpolation is, therefore, considered to be better choice for compressible multicomponent flows in the framework of WCNS. Meanwhile better choice of fully or quasi-conservative form depends on a situation because the error due to fully conservative form can be suppressed by smoothed interface and because quasi-conservative form eliminates all the numerical oscillation but has poor mass conservation.     

Curvilinear finite-volume schemes using high-order compact interpolation

During the last years, the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown. Most of high fidelity numerical schemes, in terms of low dissipative and low dispersive effects, lie on finite-difference (FD) approach. But for industrial applications, FD schemes are less robust compared to finite-volume (FV) ones. Thus the present study focuses on the development of a new compact FV scheme for two- and three-dimensional applications.The proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works. Therefore, they are more appropriate for general grids. They are based on compact interpolation to approximate interface-averaged field values using known cell-averaged values. For each interface, the interpolation coefficients are determined by matching Taylor series expansions around the interface center. Two types of schemes can be distinguished. The first one uses only the curvilinear abscissa along a mesh line to derive a sixth-order compact interpolation formulae while the second, more general, uses coordinates in a spatial three-dimensional frame well chosen. This latter is formally sixth-order accurate in a preferred direction almost orthogonal to the interface and at most fourth-order accurate in transversal directions.For non-linear problems, different approaches can be used to keep the high-order scheme. However, in the present paper, a MUSCL-like formulation was sufficient to address the presented test cases.All schemes have been modified to treat multiblock and periodic interfaces in such a way that high-order accuracy, stability, good spectral resolution, conservativeness and low computational costs are guaranteed. This is a first step to insure good scalability of the schemes although parallel performances issues are not addressed. As high frequency waves, badly resolved, could be amplified and then destabilize the scheme, compact filtering operators have been used.Numerous test cases as the linear convection of a Gaussian wave, the convection of a Lamb–Oseen vortex and the diffraction of an acoustic wave on a plane have been realized to validate the schemes. The most efficient schemes are shown to be at least fifth-order accurate on linear and non-linear convection problems. They are also less dissipative and less dispersive on non-uniform curvilinear grids than schemes using implicit interpolation with constant coefficients of the same order on uniform cartesian grids.     

A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis

A high-order accurate hybrid central-WENO scheme is proposed. The fifth order WENO scheme [G.S. Jiang, C.W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys. 126 (1996) 202–228] is divided into two parts, a central flux part and a numerical dissipation part, and is coupled with a central flux scheme. Two sub-schemes, the WENO scheme and the central flux scheme, are hybridized by means of a weighting function that indicates the local smoothness of the flowfields. The derived hybrid central-WENO scheme is written as a combination of the central flux scheme and the numerical dissipation of the fifth order WENO scheme, which is controlled adaptively by a weighting function. The structure of the proposed hybrid central-WENO scheme is similar to that of the YSD-type filter scheme [H.C. Yee, N.D. Sandham, M.J. Djomehri, Low-dissipative high-order shock-capturing methods using characteristic-based filters, J. Comput. Phys. 150 (1999) 199–238]. Therefore, the proposed hybrid scheme has also certain merits that the YSD-type filter scheme has. The accuracy and efficiency of the developed hybrid central-WENO scheme are investigated through numerical experiments on inviscid and viscous problems. Numerical results show that the proposed hybrid central-WENO scheme can resolve flow features extremely well.     

Sub-THz continuous wave generation scheme using high-order harmonics modulated lightwave

We propose a sub-THz continuous wave (CW) generation scheme using a high-order harmonics modulated lightwave (HML) to reduce an electronic dependency of a conventional double sideband suppressed carrier (DSB-SC) scheme. The electronic dependency should be overcome to increase frequency tunability of the conventional DSB-SC scheme. This is because the frequency of a local oscillator (LO), f_LO, should be one-half frequency of the frequency of a desired sub-THz CW in the conventional DSB-SC scheme. The proposed scheme is formed by adding an optical feedback loop to the conventional DSB-SC scheme. In order to verify our proposed scheme, a 120 GHz CW is generated using the LO with f_LO = 20 GHz. Based on our experimental results, we have found that the frequency of the LO can be reduced by our proposed scheme up to one-sixth (20 GHz) of 120 GHz. The 120 GHz CW generated by the proposed scheme has 52 dB higher photomixed output power with narrow spectral linewidth than that of the 120 GHz CW generated by the conventional DSB-SC scheme using the LO with f_LO = 20 GHz. Consequently, our proposed scheme can be helpful to reduce the electronic dependency of the conventional DSB-SC scheme.     

General relativistic null-cone evolutions with a high-order scheme

We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. Consequently the scheme offers more accuracy at a given computational cost compared to previous methods which are second-order accurate. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.     

A new compact scheme for parallel computing using domain decomposition

Direct numerical simulation (DNS) of complex flows require solving the problem on parallel machines using high accuracy schemes. Compact schemes provide very high spectral resolution, while satisfying the physical dispersion relation numerically. However, as shown here, compact schemes also display bias in the direction of convection – often producing numerical instability near the inflow and severely damping the solution, always near the outflow. This does not allow its use for parallel computing using domain decomposition and solving the problem in parallel in different sub-domains. To avoid this, in all reported parallel computations with compact schemes the full domain is treated integrally, while using parallel Thomas algorithm (PTA) or parallel diagonal dominant (PDD) algorithm in different processors with resultant latencies and inefficiencies. For domain decomposition methods using compact scheme in each sub-domain independently, a new class of compact schemes is proposed and specific strategies are developed to remove remaining problems of parallel computing. This is calibrated here for parallel computing by solving one-dimensional wave equation by domain decomposition method. We also provide the error norm with respect to the wavelength of the propagated wave-packet. Next, the advantage of the new compact scheme, on a parallel framework, has been shown by solving three-dimensional unsteady Navier–Stokes equations for flow past a cone-cylinder configuration at a Mach number of 4.Additionally, a test case is conducted on the advection of a vortex for a subsonic case to provide an estimate for the error and parallel efficiency of the method using the proposed compact scheme in multiple processors.     

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite-difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.     

Z-scan analysis of high-order nonlinear refraction effect induced by using elliptic Gaussian beam

The irradiance of an elliptic Gaussian beam that is high enough to excite high-order nonlinear refraction effect is used to calculate the normalized on-axis transmittance function in the z-scan technique by introducing complex beam parameters which make the calculation simpler. The transmittance formula is applied to the first-, first two-, and first three-order nonlinearities. Numerical evaluation shows that the symmetry no longer holds when using an elliptic Gaussian beam instead of a circular Gaussian beam. A distortion is observed in the central part of the curve, which decreases as ellipticity increases. Moreover, the variation of the normalized peak-valley difference decreases as ellipticity decreases.     

Retrieval of high-order susceptibilities of nonlinear metamaterials

Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime.However, existing S-parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived.Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power,high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposed approach can be widely used in the research of active metamaterials.     

Dielectric properties of glycine phosphite crystals in the model of a phase transition with inclusion of high-order invariants

Dielectric anomalies in the vicinity of the ferroelectric phase transition in nominally pure glycine phosphite (GPI) crystals and glycine phosphite crystals containing 2 mol % glycine phosphate (GP) are studied. It is revealed that the impurity-induced internal macroscopic polarization observed for GPI-GP crystals brings about smearing of the dielectric anomalies in directions both parallel and perpendicular to the axis of spontaneous polarization. The ferroelectric phase of the GPI and GPI-GP crystals is characterized by an unusual variation in the inverse permittivity in the Z direction perpendicular to the Y axis of spontaneous polarization. The temperature dependence of the inverse permittivity is described by a power expression (T _c ? T) ⁿ with an exponent n larger than unity. The experimental data are analyzed in terms of the proposed thermodynamic model with two order parameters, namely, the displacement parameter η and the order-disorder parameter P, which have different physical natures but the same symmetry and allow for coupling invariants of the ηP and η³ P types, as well as for the built-in polarization in the case of GPI-GP crystals. The experimental and theoretical dependences are in good agreement. The coefficients of bilinear and nonlinear coupling between the order parameters are determined. It is shown that the phase transition in the crystals occurs in the vicinity of the tricritical point and that the unusual behavior of the permittivity with a variation in the temperature is explained by the contribution from high-order invariants of coupling.     

Numerical modelling of ultrasonic waves in a bubbly Newtonian liquid using a high-order acoustic cavitation model

To address difficulties in treating large volumes of liquid metal with ultrasound, a fundamental study of acoustic cavitation in liquid aluminium, expressed in an experimentally validated numerical model, is presented in this paper. To improve the understanding of the cavitation process, a non-linear acoustic model is validated against reference water pressure measurements from acoustic waves produced by an immersed horn. A high-order method is used to discretize the wave equation in both space and time. These discretized equations are coupled to the Rayleigh-Plesset equation using two different time scales to couple the bubble and flow scales, resulting in a stable, fast, and reasonably accurate method for the prediction of acoustic pressures in cavitating liquids. This method is then applied to the context of treatment of liquid aluminium, where it predicts that the most intense cavitation activity is localised below the vibrating horn and estimates the acoustic decay below the sonotrode with reasonable qualitative agreement with experimental data.     

Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation

In this Letter, we present an analytical study of a high-order acoustic wave equation in one dimension, and reformulate a previously given equation in terms of an expansion of the acoustic Mach number. We search for non-trivial traveling wave solutions to this equation, and also discuss the accuracy of acoustic wave equations in terms of the range of Mach numbers for which they are valid.     

Evidence of Autler-Townes splitting in high-order nonlinear processes

We demonstrate Autler-Townes (AT) splitting of four-wave mixing in an electromagnetically induced transparency window, which results from the destructive interference between a three-photon process and a five-photon process. The primary and secondary AT splittings are achieved via induced atomic coherence in a four-level Y-type atomic system. Theoretical calculations fit well with the experimentally measured results. Such controlled multichannel splitting of nonlinear optical signals can have potential applications in optical communication and quantum information processing.     

A shock-detecting sensor for filtering of high-order compact finite difference schemes

A new shock-detecting sensor for properly switching between a second-order and a higher-order filter is developed and assessed. The sensor is designed based on an order analysis. The nonlinear filter with the proposed sensor ensures damping of the high-frequency waves in smooth regions and at the same time removes the Gibbs oscillations around the discontinuities when using high-order compact finite difference schemes. In addition, a suitable scaling is proposed to have dissipation proportional to the shock strength and also to minimize the effects of the second-order filter on the very small scales. Several numerical experiments are carried out and the accuracy of the nonlinear filter with the proposed sensor is examined. In addition, some comparisons with other filters and sensors are made.     

Necessary conditions for nonlinear excitation of a high-order mode in a single-mode optical fiber

The necessary conditions for nonlinear excitation of higher-order modes in a single-mode step-index optical fiber are analyzed. The cutoff conditions for such an optical waveguide are investigated taking into account Kerr nonlinearity. The minimal power of optical pulses required for fulfilling the necessary conditions for nonlinear excitation of higher-order modes in a single-mode step-index fiber is calculated as a function of the normalized frequency. The allowed ranges of variation of the normalized frequency and optical-radiation power are estimated. It is demonstrated that the conditions necessary for nonlinear excitation of a higher-order mode in a step-index single-mode optical fiber can be created for optical pulses shorter than 500 fs.     

A theoretical scheme for generation of nonlinear coherent states in a micromaser under intensity-dependent Jaynes-Cummings model

In this paper we propose a theoretical scheme to show the possibility of generating various families of nonlinear (f-deformed) coherent states of the radiation field in a micromaser. We show that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity–dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in a two-photon micromaser.     

Approximate step response of a nonlinear hydraulic mount using a simplified linear model

A simplified dynamic stiffness type linear model is used to analytically find the step responses of a nonlinear hydraulic mount in terms of the transmitted force and top chamber pressure. The closed form solution could be efficiently implemented with effective mount parameters, and peak value and the decay curve predictions could provide some insight into the nonlinear behavior. The analytical solutions to an ideal step input correlate well with both numerical simulations (of the same linear model) and measurements when a step-like displacement excitation is applied to fixed and free decoupler mounts.     

Enhancement of nonlinear susceptibility in a four-level tripod scheme

We propose a scheme for the enhancement of nonlinear susceptibility in a four-level tripod-type atomic system in the presence of a microwave field. With a microwave field, nonlinear susceptibility can be enhanced. Nonlinearity can also be ulteriorly enhanced by controlling the coupling field under the optimal intensity of the microwave field. The physical mechanism of the obtained giant nonlinear susceptibility is mainly based on interactions between microwave field and coupling fields. We present a physical understanding of our numerical results using a dressed-state approach and an analytical explanation.