Finite-difference Numerical Simulations Research Articles

Finite Difference Numerical Simulation of Trapped Waves in the Kunlun Fault Zone

AbstractIn this paper, we simulated the trapped waves generated by explosions in the Kunlun fault zone, using the three‐dimensional staggered‐grid finite difference algorithm. In order to improve the reliability of final fault‐zone model, we use the data of three components. The simulations indicate that the region above the depth of 1.0 km in the Kunlun fault zone produces main effects on the characteristics of the trapped waves. The S‐wave velocities and the width of fault zone have more effects on arrival times, waveforms, amplitudes and phases of the trapped waves. By simulation, the detailed structure parameters of the Kunlun fault zone are as follows: the width of shallow fault zone is 300m, and 250m in deep; The S‐wave velocity inside the fault zone is 0.98 km/s in the layers above the depth of 400 m, and that of surrounding rock is 1.70 km/s, and the Q value is 13.8. The S‐wave velocities and Q increase with depth. Beneath the depth of 1000 m, the S‐wave velocity inside the fault zone is 2.80 km/s and that of surrounding rocks is 3.3 km/s.

Guided self-assembly of integrated hollow Bragg waveguides

We describe the fabrication of integrated hollow waveguides through guided self-assembly of straight-sided, thin film delamination buckles within a multilayer system of chalcogenide glass and polymer. The process is based on silver photodoping, which was used to control both the stress and adhesion of the chalcogenide glass films. Straight, curved, crossing, and tapered microchannels were realized in parallel. The channels are cladded by omnidirectional dielectric reflectors designed for low-loss, air-core guiding of light in the 1550-1700 nm wavelength range. Loss as low as ~15 dB/cm was measured for channels of height ~2.5 mum, in good agreement with both an analytical ray optics model and finite difference numerical simulations. The loss is determined mainly by the reflectivity of the cladding mirrors, which is ~0.995 for the as-fabricated devices.

Ultrasonic propagation in cortical bone mimics

Understanding the velocity and attenuation characteristics of ultrasonic waves in cortical bone and bone mimics is important for studies of osteoporosis and fractures. Three complementary approaches have been used to help understand the ultrasound propagation in cortical bone and bone mimics immersed in water, which is used to simulate the surrounding tissue in vivo. The approaches used were Lamb wave propagation analysis, experimental measurement and two-dimensional (2D) finite difference modelling. First, the water loading effects on the free plate Lamb modes in acrylic and human cortical bone plates were examined. This theoretical study revealed that both the S0 and S1 mode velocity curves are significantly changed in acrylic: mode jumping occurs between the S0 and S1 dispersion curves. However, in human cortical bone plates, only the S1 mode curve is significantly altered by water loading, with the S0 mode exhibiting a small deviation from the unloaded curve. The Lamb wave theory predictions for velocity and attenuation were then tested experimentally on acrylic plates using an axial transmission technique. Finally, 2D finite difference numerical simulations of the experimental measurements were performed. The predictions from Lamb wave theory do not correspond to the measured and simulated first arrival signal (FAS) velocity and attenuation results for acrylic and human cortical bone plates obtained using the axial transmission technique, except in very thin plates.

Numerical simulation of the dependence of quantitative ultrasonic parameters on trabecular bone microarchitecture and elastic constants

Finite-difference numerical simulation of ultrasound propagation in complex media such as cancellous bone represents a fertile alternative to analytical approaches because it can manage the complex 3D bone structure by coupling the numerical computation with 3D numerical models of bone microarchitecture obtained from high-resolution imaging modalities. The objective of this work was to assess in silico the sensitivity of ultrasound parameters to controlled changes of microarchitecture and variation of elastic constants. The simulation software uses a finite-difference approach based on the Virieux numerical scheme. An incident plane wave was propagated through a volume of bone of approximately 5 × 5 × 8 mm 3. The volumes were reconstructed from high-resolution micro-computed tomography data. An iterative numerical scenario of “virtual osteoporosis” was implemented using a dedicated image processing algorithm in order to modify the initial 3D microstructures. Numerical computations of wave propagation were performed at each step of the process. The sensitivity to bone material properties was also tested by changing the elastic constants of bone tissue. Our results suggest that ultrasonic variables (slope of the frequency-dependent attenuation coefficient and speed of sound) are mostly influenced by bone volume fraction. However, material properties and structure also appear to play a role. The impact of modifications of the stiffness coefficients remained lower than the variability caused by structural variations. This study emphasizes the potential of numerical computations tools coupled to realistic 3D structures to elucidate the physical mechanisms of interaction between ultrasound and bone structure and to assess the sensitivity of ultrasound variables to different bone properties.

A continuum model on the nanomesa and nanowell formation in Langmuir–Blodgett ferroelectric polymeric films

Spontaneous crystalline nanomesa and nanowell formation has recently been discovered in polyvinylidene fluoride trifluoroethylene [P(VDF–TrFE)] copolymer films developed by Langmuir–Blodgett (LB) deposition. In this paper, we propose a continuum field model to analyze this remarkable phenomenon, consisting of kinematics, energetics, and kinetics of pattern formation and evolution in P(VDF–TrFE) films. Linear perturbation analysis has been carried out to analyze the stability and growth of patterns under small perturbations, and finite difference numerical simulations have been implemented to simulate the morphologies and evolutions of nanomesas and nanowells. The effects of film thickness and a number of other material parameters have been considered in our simulations, which agree well with experimental observations. We expect that our modeling and simulation methods can be used to guide the design and optimization of nanomesa and nanowell patterns for technological applications.

Ultrasonic wave propagation in cortical bone mimics

Understanding the velocity and attenuation of ultrasonic waves in cortical bone is important for studies of osteoporosis and fractures. In particular, propagation in free- and water-loaded acrylic plates, with a thickness range of around 1–6 mm, has been widely used to mimic cortical bone behavior. A theoretical investigation of Lamb mode propagation at 200 kHz in free- and water-loaded acrylic plates revealed a marked difference in the form of their velocity and attenuation dispersion curves as a function of frequency thickness product. In experimental studies, this difference between free and loaded plates is not seen. Over short measurement distances, the results for both free and loaded plates are consistent with previous modeling and experimental studies: for thicker plates (above 3–4 mm), the velocity calculated using the first arrival signal is a lateral wave comparable with the longitudinal velocity. As the plate thickness decreases, the velocity approaches the S0 Lamb mode value. Wave2000 modeling of the experimental setup agrees with experimental data. The data are also used to test a hypothesis that for thin plates the velocity approaches the corresponding S0 Lamb mode velocity at large measurement distances or when different arrival time criteria are used. [Work supported by Action Medical Research.]

Foam drainage on the microscale I. Modeling flow through single Plateau borders.

The drainage of liquid through a foam involves flow in channels, also called Plateau borders, which generally are long and slender. We model this flow by assuming the flow is unidirectional, the shear is transverse to the flow direction, and the liquid/gas interfaces are mobile and characterized by a Newtonian surface viscosity, which does not depend on the shear rate. Numerical finite difference simulations are performed, and analytical approximations for the velocity fields inside the channels and the films that separate the bubbles are given. We compare the liquid flow rates through interior channels, exterior channels (i.e., channels contacting container walls) and films. We find that when the number of exterior channels is comparable to the number of interior channels, i.e., narrow container geometries, the exterior channels can significantly affect the dynamics of the drainage process. Even for highly mobile interfaces, the films do not significantly contribute to the drainage process, unless the amount of liquid in the films is within a factor of ten of the amount of liquid in the channels.

A phase field approach in the numerical study of the elastic bending energy for vesicle membranes

In this paper, we compute the equilibrium configurations of a vesicle membrane under elastic bending energy, with prescribed volume and surface area. A variational phase field method is developed for such a problem. Discrete finite difference approximations and numerical simulations are carried out in the axial symmetrical cases. Different energetic bifurcation phenomena are discussed.

Modeling sub‐grid‐block‐scale dense nonaqueous phase liquid (DNAPL) pool dissolution using a dual‐domain approach

A dual‐domain approach is developed for calculating the advective and dispersive mass flux of chemical leaving one or more sub‐grid‐block‐scale DNAPL pool(s) in an integral finite difference numerical simulation. The contaminated zone in a simulation is divided into two fractions: one that contains DNAPL pools and one in which DNAPL is not present. With a dual‐permeability formulation the two regions may have the same or different flow properties depending on the conceptual model for pool formation, and fluids can freely flow through both domains. The local dispersive flux of contaminant away from the DNAPL pool is calculated using a well‐known analytical solution for steady state advection and dispersion. This expression is integrated analytically to give a first‐order mass transfer relationship for the total dissolution rate inside a grid block as a function of the horizontal water velocity, the transverse dispersivity, the DNAPL solubility, and the dissolved concentration in the media not containing the DNAPL. The calculated interphase mass transfer rate using a single dual‐domain integral finite difference grid block is shown to match experimental data and an analytical solution for DNAPL pool dissolution.

Analytical characterisation of amplitude-dampening and phase-shifting in air/soil heat-exchangers

This article presents the complete analytical solution for the heat diffusion of a cylindrical air/soil heat-exchanger with adiabatic or isothermal boundary condition, submitted to constant airflow with harmonic temperature signal at input. It will be shown that, depending on its thickness, the soil layer will induce either one of two kinds of amplitude-dampening and phase-shifting regimes of the periodic input signal. In particular, for a thin layer submitted to adiabatic boundary condition, it is possible to completely phase-shift the periodic input while barely dampening its amplitude, a phenomenon apparently unexploited up to now, which might give rise to interesting energy handling techniques. Analytical results are validated against a finite-difference numerical simulation model as well as against an experimental setup.

Characterizing Miscible Displacements in Heterogeneous Reservoirs Using the Karhunen–Loéve Decomposition

The article describes the application of the Karhunen–Loéve (K–L) decomposition in characterizing miscible displacements in geostatistically generated permeable media. A large number of simulation runs were performed in several heterogeneous reservoirs, each with different dimensionless scaling groups, and the spatial fluid concentrations were mapped at various times. The heterogeneous permeable media were generated geostatistically using the Matrix Decomposition Method with various degrees of permeability variations and correlation lengths. A finite difference numerical simulator (UTCHEM) has been used for this purpose. Results show that the correlation length and the permeability variation significantly affect the performance of miscible displacements and the transition between gravity-dominated and viscous-dominated displacements. The K–L decomposition was then used to determine an optimum set of eigenfunctions representing the coherent structure of all the simulated data. Results show that these complex patterns arising from a large number of simulation runs can be described by twenty dominant eigenfunctions. From these eigenfunctions and the eigenvalues associated with them, one can in principle predict the results of a simulation run without actually performing the run. These include the prediction of the fluid distribution in time and space as well as the production history curve.

Anticonvection with an inclined temperature gradient.

Anticonvection, caused by external heating from above in the presence of heat sources (or sinks) homogeneously distributed on the interface, is investigated in the presence of an imposed horizontal temperature gradient. Numerical finite-difference simulations of the finite-amplitude convective regimes have been performed for the two-layer system of fluids. The interface is assumed to be flat. We discuss different scenarios of transition between multicell regimes characteristic of a vertical temperature gradient, and unicell structures induced by horizontal gradients. The coexistence of these two regimes in sufficiently long cavities has been obtained. Regular oscillations are also predicted in other situations.

On the transient thermal behaviour of structural walls — the combined effect of time varying solar radiation and ambient temperature

The aim of the present work is to investigate the transient conduction heat transfer in structural walls. The developed finite difference numerical simulation code, which is suitable to run in conventional microcomputers, has the flexibility to incorporate a wide range of boundary and initial conditions and time-dependent forcing functions for the investigation of the transient heat transfer in walls of any design. The analysis was employed for the prediction of the dynamic thermal behaviour of two wall designs under the effect of a step temperature change and a combined time varying ambient temperature and solar radiation corresponding to typical local weather conditions. The results allow the prediction of the transient duration, the transient temperature fields as well as the quasi-steady state heat fluxes. They also allow the investigation of the dynamic effects of realistic time varying meteorological forcing functions and the strong influence of the wall surface absorptivity, something which confirms its importance as a handy instruction and research tool in the renewable and rational use of energy fields.

Growth of binary fluid convection: role of the concentration field.

The growth of convection in binary fluid mixtures out of different perturbations of the quiescent conductive state is investigated using finite-difference numerical simulations for realistic ethanol-water parameters with strong negative Soret coupling between temperature and concentration fluctuations. Several different analysis tools are used to elucidate the complex spatiotemporal behavior associated with the dramatic concentration redistribution during the transients. It shows first the competition between counterpropagating waves that initially superimpose to form standing wave perturbations. Having reached a critical amplitude an advective breaking of the concentration wave triggers a very fast flow-induced transition from standing to traveling wave convection with large phase velocity and large concentration field amplitudes. Strongly nonlinear advective mixing and weak long-time diffusive homogenization then slow down the waves.

TRACER RESPONSE IN PARTIALLY FRACTURED RESERVOIRS

ABSTRACT There is considerable interest in the petroleum industry to characterize partially fractured reservoirs and to develop an increased understanding of the physics of fluid flow in these types of reservoirs. This is because fractured reservoirs have different behavior and there exist a large number of these reservoirs that are not fully developed. This paper presents a numerical simulation study that was performed to investigate the effect of rock properties on the tracer response in partially fractured reservoirs using a finite difference numerical simulator. These properties include fracture intensity, fracture porosity and matrix permeability. The functional relationships between these parameters and the calculated effective permeabilities are also investigated. Several images, each with different probability of fracture intensity, were generated randomly. Numerical simulations of single-phase tracer transport were then performed in each of the generated fractured models. Results show that the fracture intensity, fracture porosity and matrix permeability have a significant effect on the tracer response in naturally fractured reservoirs. Depending on the reservoir properties, the results also show that the flow in partially fractured reservoirs can be either matrix-dominated or fracture-dominated. The characteristics of each regime and the conditions for its occurrence are presented.

Algorithms for 3D localization and imaging using near-field diffraction tomography with diffuse light

We introduce two filtering methods for near-field diffuse light diffraction tomography based on the angular spectrum representation. We then combine these filtering techniques with a new method to find the approximate depth of the image heterogeneities. Taken together these ideas improve the fidelity of our projection image reconstructions, provide an interesting three dimensional rendering of the reconstructed volume, and enable us to identify and classify image artifacts that need to be controlled better for tissue applications. The analysis is accomplished using data derived from numerical finite difference simulations with added noise.

磁気記憶装置ヘッド・媒体インタフェースにおける熱点温度推定法 第１報 表面温度推定式の導出

The feasibility is investigated of estimating the flash temperature of intermittent magnetic head/media contacts using the output of a magnetoresistive (MR) micro-sensor embedded in the head. On the assumption that a uniform square heat source moves on the head surface at a high speed, an apporoximate relationship between the surface temperature rise and the sensor output change is presented by applying the profile method in heat conduction theory. In order to calculate the surface temperature using this relationship, it is necessary to know the heat source width. In this paper, the width is assumed to be equal to its length that can be observed from the sensor output increasing duration. A finite difference numerical simulation is performed to verify the estimation accuracy of this method for different sensor heights in the range from 2.5 to 20 L' m. The influences of the thermal properties of the sensor surrounding material are also made clear. As a result, in the case of MR sensor NiFe and its surrounding material A12O3-TiC, the surface temperature can be estimated with an accuracy of about 10% for sensors of less than 10 u- m high and a heat source duration more than 0.5μs.

立川断層における深い地盤構造の探査

Tachikawa fault is an active fault located in the western part of the Tokyo Metropolitan area. A structure of deep sedimentary layers around the fault was explored by microtremor array measurements and an analysis of existing seismic refraction data for the purpose of estimating its effects on earthquake ground motion. It was found from the microtremor array measurements that a basement depth in S-wave profile at down-thrown side of the fault is larger than that at up-thrown side with depth difference of 1.6km. A two-dimensional model was constructed using the explosion data and the depth data on the sediments derived from the microtremor array measurements. Travel times of initial P-wave for the proposed model calculated by a finite difference ray tracing fit the observed travel times better than the model from a conventional time term analysis. We evaluated spatial variations of amplification of earthquake ground motion in the proposed model using a 2D finite difference numerical simulation. It was found that ground motion in the down-thrown side is amplified due to effects of the basement step.

On the Convective and Absolute Nature of Instabilities in Finite Difference Numerical Simulations of Open Flows

In numerical simulations of unstable flows the absolute or convective nature of the instability can be modified by numerical effects. We introduce a convective/absolute analysis of the dispersion relations associated with discretized operators. This analysis leads to conditions on the discretization parameters in order to avoid numerical transition from absolute to convective instability and vice versa. In numerical simulations of non-parallel flows, local numerical transitions, of the kind described in this paper, could lead to the wrong global dynamics.

Solitary waves in coupled nonlinear waveguides with Bragg gratings

We study solitons (strictly speaking, solitary waves) in a model of two linearly coupled waveguides with the Kerr nonlinearity and resonant gratings, neglecting the material dispersion. An effective dispersion is induced by the linear couplings between the forward and backward Bragg-scattered waves and between the two cores. First, we consider a transition from the obvious symmetric solitons to nontrivial asymmetric ones for quiescent (standing) solitons. The solutions are found in an approximate analytical form by means of the variational approximation and, independently, by direct finite-difference numerical simulations. Results produced by the two methods are in a fairly good agreement. We further establish the stability of the asymmetric solitons by direct simulations, while showing that the symmetric solitons coexisting with the asymmetric ones are always unstable. Next, we consider traveling solitary waves. We fix the frequency detuning, while the strength of the coupling between the two cores and the velocity of the moving soliton are varied. In this case the solutions are found only by direct numerical methods, revealing that moving asymmetric solitons exist and are stable. Similar to the case of the quiescent solitary waves, the symmetric solitons coexisting with the asymmetric ones prove to be always unstable.