Forward and Inverse Viscoacoustic Modelling in a Tunnel Environment

In this work, the goal is to model forward acoustic waves in a tunnel environment with attenuation and to do full waveform inversion. In reality, there is no material without attenuation. Some materials, such as rocks, have so low attenuation that, in a small domain, the waves are almost not damped at all. At the same time, there are materials with high attenuation. In an environment with such materials, the attenuation has to be taken into account in order to model the waves properly. In this study, attenuation effect is integrated into acoustic equation by using Kolsky-Futterman model ( [1], [2]) which only replaces velocity field with a complex-valued field in frequency domain. Apart from attenuation, another objective is to consider an inhomogeneous density field. Mainly, acoustic equation with a constant density field is referred to in many studies. In many cases, it may suffice to model waves appropriately. However, in reality, the density field of ground can be highly inhomogeneous. The objective is to investigate the effect of the inhomogeneity in waves, and to search for density field ρ and attenuation parameter Q as well as pressure wave velocity c using full waveform inversion. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An optimized finite element method for the analysis of 3D acoustic cavities with impedance boundary conditions

Numerical approaches studying the reduction of dispersion error for acoustic problems so far have focused on the models without impedance. Whereas, the practical acoustic problems usually involve impedance. This situation indicates that it is essential to study the numerical methods by taking into account the influence of impedance. In this work, an optimized finite element method is introduced to solve the three-dimensional steady-state acoustic problems with impedance. This technique resorts to heuristic optimization techniques to determine the integration points locations in elements. It develops a strategy to optimize the integration points locations, and makes use of adaptive genetic algorithm to achieve the best integration points locations for the construction of element matrix. By using the proposed method, a three-dimensional acoustic tube model with impedance is investigated, and the dispersion error, accuracy, convergence and efficiency of solutions are all compared to those of some existing numerical methods and reference solutions. Simultaneously, two practical cavity models are studied to verify the effectiveness and strongpoints of the proposed method as compared to existing numerical methods. Hence, the proposed method can be more widely applied to solve practical acoustic problems, yielding more accurate solutions.     

3D complex structures imaging based on acoustic wave equation

In this paper, a general expression of the 3D hybrid imaging method based on acoustic wavefield extrapolation is presented. Moreover, the planewave synthesization method is given. The numerical results of 3D shot-profile migration and planewave synthesization migration for the SEG/EAEG 3D benchmark model show the good imaging ability of the hybrid imaging method. This method can be applied in field data processing. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Level Set Methods in a Benchmark for Thermoacoustic Instabilities

Gas turbines can suffer from combustion instabilities and combustion driven oscillations. As a prestep a 3D benchmark tube geometry for the complicated interactions between acoustics and thermal heat release is investigated. For the representation of the flame surface a Level Set approach was chosen. The resulting model includes the impact of curvature on the laminar burning velocity as well as the potential flow field and underlying velocity fields due to vorticity and volume expansion across the flame front. The acoustic equations and the thermal heat release are coupled by the acoustic velocity which is also included in the flame model. A numerical simulation of this benchmark problem is presented as a first step toward optimizing or controlling the stability behavior of the system. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration of submerged floating tunnels due to moving loads

The concept of submerged floating tunnel (SFT) has become an increasingly attractive idea to cross the straits. The structural solution in this scheme includes buoyancy force on tunnel body plus tension in mooring tethers. This paper investigates the effect of submergence on the dynamic response of SFT due to moving load. The inertial effect of the fluid is accounted for by evaluating the added mass of tunnel using two and three dimensional models. It is found that fluid–structure interaction increases dynamic amplification of the tunnel deflection (in some cases very significantly). The results show that although the 3D model predicts lesser inertial contribution for surrounding fluid, it is not always possible to associate the larger response with the 2D or 3D models. The discrepancy between the results of the two models decreases as the tether stiffness increases. This indicates that the adoption of Morison’s equation for evaluating the fluid loading on the tunnel is a reasonable assumption when the tether stiffness is high. It is also found that by increasing the tether stiffness, it is possible to introduce a major reduction in the dynamic amplification of the response and by this way control the dynamic response of the SFT.     

Coupling of the Reynolds Fluid-Film Equation with the 2D Navier-Stokes Equations

The pressure field in thin fluid films can quite precisely be calculated by Reynolds fluid-film equation. In some problems, it may be useful to couple thin fluid-films with general 2D or 3D fluid flows. In the current work, we analyze the fluid flow, pressure and temperature field in a hydrodynamic journal bearing with a rectangular oil groove. Pressure and temperature in the fluid gap are calculated by means of the Reynolds equation and the 2D energy equation. Cavitation effects are taken into account by incorporating a 2-phase cavitation approach. In order to calculate the velocity and pressure field in the oil groove, the 2D Navier-Stokes equations are used; the temperature distribution in the oil groove is computed by means of the 2D energy equation. Appropriate coupling conditions for velocity, pressure and temperature are formulated in order to couple the flow in the fluid gap with the flow in the oil groove. Thermal expansion of journal shaft and bearing housing are also taken into account, since the bearing clearance changes with increasing temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Smoke flow phenomena and turbulence characteristics of tunnel fires

Gravity currents are similar in behavior with smoke flows. This work aims to provide evidence justifying the use of gravity current approach to model smoke flows downstream of the fire source. The turbulence solver available in almost all commercial CFD codes solves RANS for the flow field. To find out how well the nature of smoke flow be accurately modeled using RANS that is widely used for incompressible flows. The feasibility of using both Reynolds- and Favre-averaging schemes was numerically compared and examined in this paper. In this work, numerical simulations of a fire occurred in a 400-m longitudinally ventilated tunnel have been successfully performed using FDS version 4. Large eddy simulation is employed in this study. Although the ranges of fire size and ventilation velocity vary respectively from 0 MW to 100 MW and 0 m/s to 10 m/s, this paper focuses on the general flow and temperature fields and the turbulence characteristics. Furthermore, the turbulence kinetic energy levels of the flow in the tunnel at several locations were investigated. Since the flow field is generally induced by mechanical ventilation and combustion, the main contribution to the turbulence kinetic energy comes from its longitudinal, vertical, or their combination.     

The propagation of sound in particle models of compressible fluids

Summary. The propagation of sound in compressible fluids is described by the acoustic equations that result from the linearization of the Euler equations around a state of constant mass density and velocity zero. In this article, it is shown that a stable and convergent discretization of the acoustic wave equation for the velocity field can be recovered from the particle model of compressible fluids recently developed by the author in [Numer. Math. (1997) 76: 111–142] by linearizing the equations of motion for the particles. For particles of proper shape, this discretization is second order accurate, and with an obvious modification of the basic particle model, one can even reach an arbitrarily high order of convergence. Received January 24, 2000 / Published online November 8, 2000     

2D Continuous Wavelet Transform of potential fields due to extended source distributions

We analyse the real Continuous Wavelet Transform 2D (CWT2D) of potential fields for the investigation of potential field singularities. We focus our attention to extended geological sources, in order to verify the reliability of this method with realistic fields. 3D space-scale representation (3D Scalogram) related to synthetic models were generated, showing the Wavelet Transform Modulus Maxima (WTMM) at each scale. The WTMM are related to the shape of the source, so defining some sort of source boundary analysis through the CWT. Wavelets of different order may help to gain resolution and define source features. Selecting a range of scales where the sources behave as if they are approximately isolated, the depth to the source may be estimated basing on the property that the lines joining the modulus maxima of the wavelet coefficients at different scales (WTMML) intersect each other at the edges of the causative body. Therefore, it is possible to manage the information contained in the wavelet transform of fields related to extended sources. In the real case of the anomaly gravity map of the Vesuvius area (Italy), we estimated the depth of the Mesozoic carbonate basement in the Pompei Basin. We showed also how the WTMML information can be integrated to that of another multiscale method, the Depth from Extreme Points (DEXP) transformation, which is also related to the source density distribution of a given region.     

Coupling 3D and 1D fluid-structure interaction models for blood flow simulations

Three-dimensional (3D) simulations of blood flow in medium to large vessels are now a common practice. These models consist of the 3D Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall structure. However, it is still computationally unaffordable to simulate very large sections, let alone the whole, of the human circulatory system with fully 3D fluid-structure interaction models. Thus truncated 3D regions have to be considered. Reduced models, one-dimensional (1D) or zero-dimensional (0D), can be used to approximate the remaining parts of the cardiovascular system at a low computational cost. These models have a lower level of accuracy, since they describe the evolution of averaged quantities, nevertheless they provide useful information which can be fed to the more complex model. More precisely, the 1D models describe the wave propagation nature of blood flow and coupled with the 3D models can act also as absorbing boundary conditions. We consider in this work the coupling of a 3D fluid-structure interaction model with a 1D hyperbolic model. We study the stability of the coupling and present some numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

SPEW: Synthetic Populations and Ecosystems of the World

Agent-based models (ABMs) simulate interactions between autonomous agents in constrained environments over time and are often used for modeling the spread of infectious diseases. ABMs use information about agents and their environments as input, together referred to as a “synthetic ecosystem.” Previous approaches for generating synthetic ecosystems have some limitations: they are not open-source, cannot be adapted to new or updated input data sources, or do not allow for alternative methods for sampling agent characteristics and locations. We introduce a general framework for generating synthetic ecosystems, called “Synthetic Populations and Ecosystems of the World” (SPEW). SPEW lets researchers choose from a variety of sampling methods for agent characteristics and locations and is implemented as an open-source R package. We analyze the accuracy and computational efficiency of SPEW, given different sampling methods for agent characteristics and locations, and provide a suite of statistical and graphical tools to screen our generated ecosystems. SPEW has generated over five billion human agents across approximately 100,000 geographic regions in over 70 countries available online.     

Small oscillations of an emulsion of two weakly viscous compressible liquids

The small oscillations of an emulsion of two weakly viscous compressible liquids in an external acoustic field are studied. The structure of the mixture is assumed to be periodic with a sufficiently by small cell size. An integro-differential acoustic equation and an expression for the mean velocity are derived by the two-scale convergence method and the strong convergence of the difference in the velocities and the difference in the velocity gradients of the prelimiting and limiting problems (the initial problem and the averaged problem) to zero in L₂ is proved. The elements of the dynamic “filtration matrix”, that is, of the kernel of the convolution of the acoustic equation, are calculated by the finite volume methods.     

A new model for the acoustic wake effect in aerosol acoustic agglomeration processes

The acoustic wake effect has been considered the main agglomeration mechanism in the aerosol acoustic agglomeration processes. However, the existing theoretical model for the acoustic wake effect, which was proposed half century ago, is not accurate enough and overestimates the perturbation velocity in the vicinity of particles by as high as approximately 50%. In this paper, a new model for the acoustic wake effect is established, in which an approximate expression is constructed to describe the perturbation velocity. The newly developed model has been verified to be more accurate than the existing model by both theoretical analysis of boundary conditions and computational fluid dynamics simulation. The trajectories of two particles in a horizontal sound field are calculated based on the new model and the existing model. The results show that the new model corrects the range of initial orientation angle for two particles to successfully agglomerate, which was overestimated in the existing model. Moreover, the collision efficiency of two different-sized particles under the acoustic wake effect is found to be larger in the simulation by the new model than that by the existing model. The new model can be used as a reasonably accurate tool not only for calculating the agglomeration of two particles, but also for the numerical simulation of acoustic agglomeration of an aerosol containing a large number of particles due to its low computational cost.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

Stochastic dynamo in critical situations

Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established.     

Comparative study of 1D, 2D and 3D simplified gas kinetic schemes for simulation of inviscid compressible flows

With assumption that all the particles in the phase velocity space are concentrated on a circle and on a sphere, the circular function-based gas kinetic scheme and sphere function-based gas kinetic scheme have been developed by Shu and his coworkers [21], [22], [23]. These schemes are simpler than the Maxwellian function-based gas kinetic schemes. The simplicity is due to the fact that the integral domain of phase velocity of circular function and sphere function is a finite region while the integral domain of Maxwellian distribution function is infinite. In this work, the 1D delta function-based gas kinetic scheme is also developed to form a complete set of the simplified gas kinetic schemes. The 1D, 2D and 3D simplified gas kinetic schemes can be viewed as the truly 1D, 2D and 3D flux solvers since they are based on the multi-dimensional Boltzmann equation. On the other hand, to solve the 3D flow problem, the tangential velocities are needed to be approximated by some ways for the 1D and 2D simplified gas kinetic schemes, and to solve the 1D flow problem, the tangential velocities should be taken as zero for the 2D and 3D simplified gas kinetic schemes. The performances of these three schemes for simulation of inviscid compressible flows are investigated in this work by their application to solve the test problems from 1D to 3D cases. Numerical results showed that the efficiency of the delta function-based gas kinetic scheme is slightly superior to that of the circular function- and sphere function-based gas kinetic schemes, while its stability is inferior significantly to the latter. For simulation of the 3D hypersonic flows, the sphere function-based gas kinetic scheme could be the best choice.     

Global Regularity of 2D Leray-Alpha Regularized Tropical Climate Models

In this paper, we establish the global regularity of 2D leray-alpha regularized tropical climate models. The global strong solution to the system with a half Laplacian of the first baroclinic model of velocity $(\Lambda v)$ and thermal diffusion $(-\Delta\theta)$ or with only the dissipation of the barotropic mode $(-\Delta u)$ are obtained.     

Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models

The fluid structure interaction mechanism in vascular dynamics can be described by either 3D or 1D models, depending on the level of detail of the flow and pressure patterns needed for analysis. A successful strategy that has been proposed in the past years is the so-called geometrical multiscale approach, which consists of coupling both 3D and 1D models so as to use the former only in those regions where details of the fluid flow are needed and describe the remaining part of the vascular network by the simplified 1D model.In this paper we review recently proposed strategies to couple the 3D and 1D models, and within the 3D model, to couple the fluid and structure sub-problems. The 3D/1D coupling strategy relies on the imposition of the continuity of flow rate and total normal stress at the interface. On the other hand, the fluid–structure coupling strategy employs Robin transmission conditions. We present some numerical results and show the effectiveness of the new approaches.     

The 2D magnetohydrodynamic system with Euler-like velocity equation and partial magnetic diffusion

When the velocity equation of the incompressible 2D magnetohydrodynamic (MHD) system is inviscid, the global well-posedness and stability problem in the whole space ${\mathbb{R}}^2$ case remains an extremely challenging open problem. Broadman, Lin, and Wu (SIAM J. Math. Anal. 52(5) (2020): 5001-5035) were able to establish the global well-posedness and stability near a background magnetic field when there is damping in one velocity component. Their work exploited the stabilizing effect of the background magnetic field. This paper presents new progress. We are able to prove the global well-posedness and stability even when the magnetic diffusion is degenerate and only in the vertical direction. The velocity equation is still inviscid and has damping only in the vertical component. The proof of this new result overcomes two main difficulties, the potential rapid growth of the velocity due to the lack of dissipation or horizontal damping and the control of nonlinearity associated with the magnetic field. By discovering the key hidden smoothing effects and incorporating them in the construction of a two-layered energy function, we are able to obtain uniform bounds on the solution in the H³-norm when the initial perturbation is near the background magnetic field. In addition, we prove that certain Lebesgue and Sobolev norms of the solution approach zero as time approaches infinity.     

基于系统识别方法的围岩弹性模量及水平地应力反演分析

利用有限元软件建立隧道开挖正演模型,基于新奥法隧道施工现场实测围岩收敛数据,采用灵敏度分析建立了参数调整算法,利用系统识别方法对隧道围岩弹性模量及水平地应力进行了反演分析,并讨论了初始值的影响.结果表明,系统识别反演分析法具有自适应能力强、反演分析过程收敛计算稳定性好和计算速度快等优点,在隧道及地下工程领域具有广阔的应用前景.