Three-dimensional Numerical Experiments Research Articles

Edge-promoting reconstruction of absorption and diffusivity in optical tomography

In optical tomography a physical body is illuminated with near-infrared light and the resulting outward photon flux is measured at the object boundary. The goal is to reconstruct internal optical properties of the body, such as absorption and diffusivity. In this work, it is assumed that the imaged object is composed of an approximately homogeneous background with clearly distinguishable embedded inhomogeneities. An algorithm for finding the maximum a posteriori estimate for the absorption and diffusion coefficients is introduced assuming an edge-preferring prior and an additive Gaussian measurement noise model. The method is based on iteratively combining a lagged diffusivity step and a linearization of the measurement model of diffuse optical tomography with priorconditioned LSQR. The performance of the reconstruction technique is tested via three-dimensional numerical experiments with simulated data.

Flow separation control in open-channel bends

The investigation of fluid flow in sharp open-channel bends is key to controlling undesired sedimentation in natural river reaches. The difficulties are associated with controlling the flow separation in meanderings. Flow separation decreases the width of the flow, and consequently, the conveyance capacity while increasing erosion and mixing. This study proposes a novel approach to reduce the flow separation at the inner banks of sharp open-channel bends. Three-dimensional numerical experiments were conducted. To find the most reliable procedure, five turbulence models were examined. The employed numerical approach is formulated within the framework of the finite volume method and the volume of fluid (VOF) technique to solve the Navier–Stokes equations. Water levels and velocity profiles are obtained in different sections of the channel and are compared to experimental studies of a 90° sharp open-channel bend. A close agreement is observed using the RSM (Reynolds stress model) turbulence model. Moreover, the evaluation of acquired velocity profiles demonstrates that in a regular bend, the lowest velocity occurs near the inner bank, where it has a flow separation tendency. The same numerical procedure is employed to simulate water flow through a sharp converging open-channel bend. The measurements of velocity profiles and velocity vectors in the curved sections support the idea that decreasing the channel width considerably reduces the overall velocity variations in cross-sectional areas of the test case and is effective to control flow separation.

Three-dimensional finite element numerical simulation and physical experiment for magnetism-stress detecting in oil casing

The casing damage has been a big problem in oilfield production. The current detection methods mostly are used after casing damage, which is not very effective. With the rapid development of China’s offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because the cost of offshore oil well is very high, the casing damage will cause huge economic losses. What’s more, it can also bring serious pollution to marine environment. So the effective methods of detecting casing damage are required badly. The accumulation of stress is the main reason for the casing damage. Magnetic anisotropy technique based on counter magnetostriction effect can detect the stress of casing in real time and help us to find out the hidden dangers in time. It is essential for us to prevent the casing damage from occurring. However, such technique is still in the development stage. Previous studies mostly got the relationship between stress and magnetic signals by physical experiment, and the study of physical mechanism in relative magnetic permeability connecting the stress and magnetic signals is rarely reported. The present paper uses the ANSYS to do the three-dimensional finite element numerical simulation to study how the relative magnetic permeability works for the oil casing model. We find that the quantitative relationship between the stress’s variation and magnetic induction intensity’s variation is: Δδ = K* ΔB, K = 8.04×109, which is proved correct by physical experiment.

Extreme Tsunami Inundation at Babi Island due to Flores Earthquake Induced Tsunami in 1992

In this paper we investigated the phenomenon of extreme run-up at Babi Island in Indonesia caused by the 1992 Flores earthquake (Mw = 7.8) using a series of three-dimensional numerical modeling experiments. Simulations were carried out to investigate how much the presence/absence of the coast of Flores affects the generation of the extreme inundation at Babi Island through the reflection process of tsunami waves.

Performance Enhancement of Pharmacokinetic Diffuse Fluorescence Tomography by Use of Adaptive Extended Kalman Filtering.

Due to both the physiological and morphological differences in the vascularization between healthy and diseased tissues, pharmacokinetic diffuse fluorescence tomography (DFT) can provide contrast-enhanced and comprehensive information for tumor diagnosis and staging. In this regime, the extended Kalman filtering (EKF) based method shows numerous advantages including accurate modeling, online estimation of multiparameters, and universal applicability to any optical fluorophore. Nevertheless the performance of the conventional EKF highly hinges on the exact and inaccessible prior knowledge about the initial values. To address the above issues, an adaptive-EKF scheme is proposed based on a two-compartmental model for the enhancement, which utilizes a variable forgetting-factor to compensate the inaccuracy of the initial states and emphasize the effect of the current data. It is demonstrated using two-dimensional simulative investigations on a circular domain that the proposed adaptive-EKF can obtain preferable estimation of the pharmacokinetic-rates to the conventional-EKF and the enhanced-EKF in terms of quantitativeness, noise robustness, and initialization independence. Further three-dimensional numerical experiments on a digital mouse model validate the efficacy of the method as applied in realistic biological systems.

An Adaptive Finite Element Heterogeneous Multiscale Method for Stokes Flow in Porous Media

A finite element heterogeneous multiscale method is proposed for solving the Stokes problem in porous media. The method is based on the coupling of an effective Darcy equation on a macroscopic mesh with unknown permeabilities recovered from micro finite element calculations for Stokes problems on sampling domains centered at quadrature points in each macro element. The numerical method accounts for nonperiodic microscopic geometry that can be obtained from a smooth deformation of a reference pore sampling domain. The computational work is nevertheless independent of the small size of the pore structure. A priori error estimates reveal that the overall accuracy of the numerical scheme is limited by the regularity of the solutions of the Stokes microproblems. This regularity is low for a typical situation of nonconvex microscopic pore geometries. We therefore propose an adaptive scheme with micro-macro mesh refinement driven by residual-based indicators that quantify both the macro- and microerrors. A posteriori error analysis is derived for the new method. Two- and three-dimensional numerical experiments confirm the robustness and the accuracy of the adaptive method.

Simulation of elastic wave propagation in layered materials by the method of fundamental solutions

In this paper, the method of fundamental solutions (MFS) is applied in combination with the domain decomposition method to the simulation of elastic wave propagation in layered materials. The domain of the problem under consideration is decomposed into several sub-domains. In each sub-domain, the solution is approximated separately by the MFS formulation. At the sub-domain interfaces, continuity of the displacement and traction is imposed as the boundary conditions. The validity of this approach is demonstrated through a series of two- and three-dimensional numerical experiments.

Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid–structure interaction

We propose a unified convergence analysis of the generalized Schwarz method applied to a linear elliptic problem for a general interface (flat, cylindrical or spherical) in any dimension. In particular, we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions. We also provide a general procedure to obtain estimates of the optimized interface symbols within the constants. We apply such general results to a simple fluid---structure interaction model problem given by the interaction between an incompressible, inviscid fluid and the wave equation. Finally, we assess the effectiveness of the theoretical findings through three-dimensional numerical experiments in the haemodynamic context, obtained by solving the coupling between the Navier---Stokes equations and the linear infinitesimal elasticity.

Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: theory and numerical experiments

A general Nitsche method, which encompasses symmetric and non-symmetric variants, is proposed for frictionless unilateral contact problems in elasticity. The optimal convergence of the method is established both for two and three-dimensional problems and Lagrange affine and quadratic finite element methods. Two and three-dimensional numerical experiments illustrate the theory.

Asymmetric three-dimensional topography over mantle plumes.

The role of mantle-lithosphere interactions in shaping surface topography has long been debated. In general, it is supposed that mantle plumes and vertical mantle flows result in axisymmetric, long-wavelength topography, which strongly differs from the generally asymmetric short-wavelength topography created by intraplate tectonic forces. However, identification of mantle-induced topography is difficult, especially in the continents. It can be argued therefore that complex brittle-ductile rheology and stratification of the continental lithosphere result in short-wavelength modulation and localization of deformation induced by mantle flow. This deformation should also be affected by far-field stresses and, hence, interplay with the 'tectonic' topography (for example, in the 'active/passive' rifting scenario). Testing these ideas requires fully coupled three-dimensional numerical modelling of mantle-lithosphere interactions, which so far has not been possible owing to the conceptual and technical limitations of earlier approaches. Here we present new, ultra-high-resolution, three-dimensional numerical experiments on topography over mantle plumes, incorporating a weakly pre-stressed (ultra-slow spreading), rheologically realistic lithosphere. The results show complex surface evolution, which is very different from the smooth, radially symmetric patterns usually assumed as the canonical surface signature of mantle upwellings. In particular, the topography exhibits strongly asymmetric, small-scale, three-dimensional features, which include narrow and wide rifts, flexural flank uplifts and fault structures. This suggests a dominant role for continental rheological structure and intra-plate stresses in controlling dynamic topography, mantle-lithosphere interactions, and continental break-up processes above mantle plumes.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

Abstract. Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

A direct sampling method for inverse electromagnetic medium scattering

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data.

PLASMA JETS AND ERUPTIONS IN SOLAR CORONAL HOLES: A THREE-DIMENSIONAL FLUX EMERGENCE EXPERIMENT

A three-dimensional numerical experiment of the launching of a hot and fast coronal jet followed by several violent eruptions is analyzed in detail. These events are initiated through the emergence of a magnetic flux rope from the solar interior into a coronal hole. We explore the evolution of the emerging magnetically-dominated plasma dome surmounted by a current sheet and the ensuing pattern of reconnection. A hot and fast coronal jet with inverted-Y shape is produced that shows properties comparable to those frequently observed with EUV and X-Ray detectors. We analyze its 3D shape, its inhomogeneous internal structure, and its rise and decay phases, lasting for some 15-20 min each. Particular attention is devoted to the field-line connectivities and the reconnection pattern. We also study the cool and high-density volume that appears encircling the emerged dome. The decay of the jet is followed by a violent phase with a total of five eruptions. The first of them seems to follow the general pattern of tether-cutting reconnection in a sheared arcade, although modified by the field topology created by the preceding reconnection evolution. The two following eruptions take place near and above the strong field-concentrations at the surface. They show a twisted, \Omega-loop like rope expanding in height, with twist being turned into writhe, thus hinting at a kink instability (perhaps combined with a torus-instability) as the cause of the eruption. The succession of a main jet ejection and a number of violent eruptions that resemble mini-CME's and their physical properties suggest that this experiment may provide a model for the blowout jets recently proposed in the literature.

Effects of tidally induced eddies on sporadic Kuroshio-water intrusion (kyucho)

The sudden intrusion of Kuroshio warm water into the Bungo Channel (kyucho) occurs mainly at neap tides during summer, suggesting that tidal mixing is one of the essential factors regulating kyucho. In order to clarify the physical mechanisms responsible for the regulation of kyucho, we carry out non-hydrostatic three-dimensional numerical experiments allowing Kuroshio warm water to intrude into a strong tidal mixing region. It is shown that the Kuroshio warm water can (or cannot) pass through the tidal mixing regions off the east coast of the Bungo Channel during neap (or spring) tides. The analysis of the dynamic balance off the east coast of the Bungo Channel shows that tidal residual currents generated by tidal flow interaction with complicated land configurations off the east coast of the Bungo Channel can also play an important role in regulating kyucho. In order to assess separately the effects of tidal mixing and tidal residual currents on kyucho, we incorporate the parameterized vertical mixing and tidal stresses into the numerical model instead of tidal currents. It is demonstrated that tidal mixing cannot by itself block the northward intrusion of Kuroshio warm water, and that an additional effect induced by tidal residual eddies equivalent to horizontal mixing is needed to regulate kyucho. This strongly suggests that the basin–ocean water exchange processes in areas with complicated land configurations can only be reproduced by taking into account the effects of tidal residual eddies on a 1-km scale in addition to tidal mixing effects evaluated by microstructure measurements.

On the measurement of the turbulent diffusivity of a large-scale magnetic field

AbstractWe argue that a method developed by Ångström (Ann. Phys. Chem., vol. 114, 1861, pp. 513–530) to measure the thermal conductivity of solids can be adapted to determine the effective diffusivity of a large-scale magnetic field in a turbulent electrically conducting fluid. The method consists of applying an oscillatory source and measuring the steady-state response. We illustrate this method in a two-dimensional system. This geometry is chosen because it is possible to compare the results with independent methods that are restricted to two-dimensional flows. We describe two variants of this method: one (the ‘turbulent Ångström method’) that is better suited to laboratory experiments and a second (the ‘method of oscillatory sines’) that is effective for numerical experiments. We show that, if correctly implemented, all methods agree. Based on these results we argue that these methods can be extended to three-dimensional numerical simulations and laboratory experiments.

An $H_\mathsf{div}$-Based Mixed Quasi-reversibility Method for Solving Elliptic Cauchy Problems

This work considers the Cauchy problem for a second order elliptic operator in a bounded domain. A new quasi-reversibility approach is introduced for approximating the solution of the ill-posed Cauchy problem in a regularized manner. The method is based on a well-posed mixed variational problem on $H^1\times H_\mathsf{div}$ with the corresponding solution pair converging monotonically to the solution of the Cauchy problem and the associated flux, if they exist. It is demonstrated that the regularized problem can be discretized using Lagrange and Raviart--Thomas finite elements. The functionality of the resulting numerical algorithm is tested via three-dimensional numerical experiments based on simulated data. Both the Cauchy problem and a related inverse obstacle problem for the Laplacian are considered.

Evaluation of the Physical and Chemical Properties of Eyjafjallajökull Volcanic Plume Using a Cloud-Resolving Model

The Eyjafjallajokull volcanic eruption, which occurred on April 14, 2010, caused many environmental, air traffic and health problems. An attempt has been made to demonstrate for the first time that certain improvements could be made in the quantitative prediction of the volcanic ash parameters, and in the accounting of the processes in the immediate vicinity of the volcano, using a cloud-resolving model. This type of explicit modeling by treatment of volcanic ash and sulfate chemistry parameterization, with input of a number parameters describing the volcanic source, is the way forward for understanding the complex processes in plumes and in the future plume dispersion modeling. Results imply that the most significant microphysical processes are those related to accretion of cloud water, cloud ice and rainwater by snow, and accretion of rain and snow by hail. The dominant chemical conversion rates that give a great contribution to the sulfate budget are nucleation and dynamic scavenging and oxidation processes. A three-dimensional numerical experiment has shown a very realistic simulation of volcanic ash and other chemical compounds evolution, with a sloping structure strongly influenced by the meteorological conditions. In-cloud oxidation by H2O2 is the dominant pathway for SO2 oxidation and allows sulfate to be produced within the SO2 source region. The averaged cloud water pH of about 5.8 and rainwater pH of 4.5 over simulation time show quantitatively how the oxidation may strongly influence the sulfate budget and acidity of volcanic cloud. Compared to observations, model results are close in many aspects. Information on the near field volcanic plume behavior is essential for early preparedness and evacuation. This approach demonstrates a potential improvement in quantitative predictions regarding the volcanic plume distribution at different altitudes. It could be a useful tool for modeling volcanic plumes for better emergency measures planning.

Tsunami Inundation Simulation of a Built-Up Area Using Equivalent Resistance Coefficient

An equivalent resistance coefficient that includes the effect of drag caused by buildings as well as the bottom friction effect was investigated for two-dimensional inundation simulation of built-up areas with relatively coarse grids. In order to quantify the equivalent resistance coefficient for a given built-up area, we performed laboratory experiments and three-dimensional numerical experiments of steady and uniform flows influenced by square unsubmerged piers spaced at equal intervals in the longitudinal and transverse directions. The Manning's n, which represents the equivalent resistance coefficient, was evaluated by inputting experimental data into the Manning's equation. A semi-analytical formula for the n value under experimental conditions was derived via momentum analysis that included drag interaction effects. The n values resulting from laboratory experimental data, the three-dimensional numerical data, and the semi-analytical formula agreed well with each other. From these results, we found that the equivalent resistance coefficient n value is strongly dependent on the intervals between piers and increases according to water depth to the 2/3 power. In addition, as an application of the proposed n formula to the inundation model, we performed a simulation of a tsunami inundation on Imwon Harbor on the east coast of Korea.

Quasi-Static Small-Strain Plasticity in the Limit of Vanishing Hardening and Its Numerical Approximation

The quasi-static rate-independent evolution of the Prager–Ziegler-type model of plasticity with hardening is shown to converge to the rate-independent evolution of the Prandtl–Reuss elastic/perfectly plastic model. Based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of $\Gamma$-convergence for rate-independent systems. An unconditionally convergent numerical scheme is devised and two- and three-dimensional numerical experiments are presented. A two-sided energy inequality is a posteriori verified to document experimental convergence rates.

Magnetic flux emergence: a precursor of solar plasma expulsion

Aims. We model the emergence of magnetized plasma from the top of the convection zone to the lower corona. We investigate the eruption of coronal flux ropes above emerging flux regions.Methods. We performed three-dimensional numerical experiments in which the time-dependent and resistive equations of MHD are solved self-consistently, using the Lare3D code.Results. A subphotospheric magnetic flux tube rises from the convectively unstable layer into the solar surface, followed by the formation and eruption of a new flux rope into the corona. Firstly, we examined the case where the corona is field-free. The expansion of the emerging field forms an envelope sheath that surrounds the newly formed flux rope. The erupting ropes are confined by the envelope field. The eruptions are driven by the gradient of the gas pressure and the tension of fieldlines that reconnect within the emerging flux region. The amount of the initial twist of the emerging field and the dense plasma that is lifted up, determine the height-time profile of the erupting ropes. Secondly, we examined the case of emergence into a pre-existing magnetic field in the upper solar atmosphere. A variety of different ambient field configurations was used in the experiments. External reconnection between the emerging and the pre-existing field may result in the removal of sufficient flux from the interacting fields and the full ejection of the flux ropes. Conclusions. The results indicate that the relative contact angle of the interacting flux systems and their field strengths are crucial parameters that ultimately affect the evolution of the eruption of the rope into the higher solar atmosphere. One important result is that for any contact angle that favors reconnection, ejective eruptions occur earlier when the ambient field is relatively strong. In many cases, the erupting plasma adopts an S-like configuration. The sigmoidal structure accelerates during the fast eruption of the rope. The acceleration is enhanced by the external and internal reconnection of fieldlines during the rising motion of the rope. A key result is that in the reconnection-favored cases, the flux ropes experience ejective eruptions when the envelope flux is reduced (owing to removal by external reconnection) below that of the erupting flux rope. If the envelope flux stays higher than the erupting flux, the magnetic flux rope remains confined by the envelope field.