Source Boundary Conditions Research Articles

Numerical Solution of Two-Dimensional Solute Transport System Using Operational Matrices

In this study, the numerical solution of the two-dimensional solute transport system in a homogeneous porous medium of finite length is obtained. The considered transport system has the terms accounting for advection, dispersion and first-order decay with first-type source boundary conditions. Initially, the aquifer is considered solute free, and a constant input concentration is considered at inlet boundary. The solution is describing the solute concentration in rectangular inflow region of the homogeneous porous media. The numerical solution is derived using a powerful method, viz. spectral collocation method. The numerical computation and graphical presentations exhibit that the method is effective and reliable during the solution of the physical model with complicated boundary conditions even in the presence of reaction term.

Petroleum system modeling and assessment of the remaining hydrocarbon potential in the eastern part of Drava Depression

The eastern part of the Drava Depression presents a relatively small part within the Croatian part of the Pannonian Basin. A confined part within the eastern part of the Drava Depression with a working petroleum system but few hydrocarbon accumulations was selected for the evaluation of the remaining hydrocarbon potential. Four subsurface models were built with different levels of detail on which determination of source rock maturity, assessment of potential, and finally, volumes of the potentially accumulated hydrocarbons were estimated. In addition, several case scenarios, regarding source rock properties and boundary conditions were addressed to present the risk points in the model. Results proved that the amounts of hydrocarbons generated ([Formula: see text] of oil and [Formula: see text] of gas) and accumulated ([Formula: see text] of oil and [Formula: see text] of gas) in the subsurface strongly support further exploration efforts even for the conservative modeling parameters (low heat flow [HF] and moderate total organic carbon values). A set of scenarios was also modeled including different HF, total organic content, and kinetic values each with significant impact for the final model result.

Validation of a wide-angle parabolic model for shallow-focus ultrasound transducers

Recently, a novel numerical method was developed for a wide-angle parabolic equation which accommodates steep gradients and discontinuities in the pressure distribution of the source boundary condition (Soneson, IEEE Trans Ultrason., Ferroelectr., Freq. Control 64, pp. 679–687, 2017). The method allows rapid computation of acoustic fields with improved diffraction modeling capability over the standard parabolic approximation of the Helmholtz equation with no additional computational overhead, and is free from oscillatory artifacts which previously precluded the use of wide-angle models with discontinuous sources. In this work the wide-angle model, using the expression of a converging spherical wave (with a sharp cutoff at the edge of the active area) as the source boundary condition, is validated against measurements obtained using a 200 μm membrane hydrophone. The ultrasound field was produced by a single-element transducer with f-number 0.7 at 1.5 MHz, which was selected to test the wide angle model’s a...

A simplified physically-based model for coastal dike and barrier breaching by overtopping flow and waves

The simplified physically-based breach model, DLBreach, has been developed to simulate the overtopping breaching of coastal dikes and barriers, which can occur either from the sea side or the bay side. The breaching process is divided into two stages: intensive breaching and general inlet evolution, in which the flows are calculated using the weir flow equation and the Keulegan equation, respectively. The Keulegan equation is a simplified energy equation for steady nonuniform flow with local head loss due to channel contraction and expansion, revised herein by adding the wind driving force. Empirical formulas are adopted to calculate phase-averaged wave overtopping discharge, wave setup, and wind setup/setdown. The wave overtopping discharge is combined with the surge overflow discharge, and the wave setup and wind setup/setdown are added to the sea and bay water levels for the hydrodynamic and sediment routing. Alongshore sediment is considered as a source boundary condition for the non-equilibrium sediment transport model at the breach. The model has been tested using the 94’ field experiment of sea dike breaching by overflow in the Zwin Channel Estuary, a laboratory experiment of sea dike breaching initiated by wave overtopping, and a field observation of the eight-day breaching and closure event of the Mecox Inlet at eastern Long Island of New York during Sept. 10–18, 1985. The model results agree generally well with the measurements.

Modeling pulsed laser ablation of aluminum with finite element analysis considering material moving front

During the pulsed laser ablation (PLA) of solid materials, the surface of the target material progressively recedes which in turn necessitates to account for the moving front boundary in the formulation of the laser heat conduction problem. Hence, developing an accurate predictive simulation model that captures the material moving front and updates simultaneously the laser source boundary conditions is an important and yet challenging task. In this paper, the PLA of aluminum is formulated and modeled with finite element analysis (FEA) that considers the instant material removal during the ablation process. Here, the implementation of such an FEA enables a strong coupling between the progressive surface recession (i.e., the shape change of the target material) and the laser heat conduction. Moreover, the proposed numerical simulation model not only predicts the progressive surface recession due to the material evaporation in the low laser fluence regime, but it also captures the ablation depth due to the material phase explosion in the high laser fluence regime. In addition, the temperature-dependent material and optical properties of the aluminum target are considered in the simulation. With nanosecond Nd:YAG 266 and 193nm laser pulses, simulations are performed for the PLA of aluminum under various laser fluence. The predicted ablation depths under low laser fluence clearly show better agreement with experimental data, when compared to other predictions based on the hydrodynamics simulation model. Furthermore, the predicted threshold of the material phase transition in the high laser fluence regime also shows a good degree of consistency with experimental data.

Extending the Utility of the Parabolic Approximation in Medical Ultrasound Using Wide-Angle Diffraction Modeling.

Wide-angle parabolic models are commonly used in geophysics and underwater acoustics but have seen little application in medical ultrasound. Here, a wide-angle model for continuous-wave high-intensity ultrasound beams is derived, which approximates the diffraction process more accurately than the commonly used Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation without increasing implementation complexity or computing time. A method for preventing the high spatial frequencies often present in source boundary conditions from corrupting the solution is presented. Simulations of shallowly focused axisymmetric beams using both the wide-angle and standard parabolic models are compared to assess the accuracy with which they model diffraction effects. The wide-angle model proposed here offers improved focusing accuracy and less error throughout the computational domain than the standard parabolic model, offering a facile method for extending the utility of existing KZK codes.

Numerical Solution of One-Dimensional Finite Solute Transport System with First Type Source Boundary Condition

In this article, Chebyshev collocation method is used to reduce the one-dimensional advection–dispersion equation having source/sink term with given boundary conditions and initial condition into a system of ordinary differential equations which are solved using finite difference method. The solution profile of normalized solute concentration factor for both conservative and non-conservative systems are calculated numerically which are presented through graphs for different particular cases. The salient feature of this article is the comparison of the trend of numerical solution with the existing analytical solution thereby validating our considered numerical technique.

Effect of random fracture aperture on the transport of colloids in a coupled fracture-matrix system

A variable aperture model, including the random variation of fracture aperture as against the conventional parallel plate model, has been developed to adequately examine the transport of colloids/suspended particles in a single coupled fracturematrix system. Rather than relying on a complex geostatistical method for an accurate representation of fracture aperture, which requires an enormous field data and resource for its validation, a simple statistical method (linear congruential generator) is implemented in the present article. The random variation of fracture aperture is an honest representation of the unpredictable geometry/ morphology of fracture aperture in comparison with widely applied the conventional parallel plate model or the simple mathematical functions based on fractal theory (self-affine structures). A considerable number of parameters are involved in investigating the extent of penetration of colloids into the rock matrix, which creates complexity and ambiguity in the analysis. To overcome this problem, a single parameter “Maximum Penetration Factor” has been introduced for simple and reliable assessment of diffusion of colloids within the rock matrix. Additionally, a non-dimensional parameter ‘Matrix Mitigation Factor’ has been introduced in the present study, which can provide a means of evaluating the diffusion of suspended particles within the rock matrix when it comes to real time applications like microbial enhanced recovery (MEOR) and chemical enhanced recovery (CEOR) in the petroleum industry (nanoparticles and nanofluids). A semi-implicit finite difference model has been adopted for solving the coupled partial differential equations in the present numerical study. Finally, Neumann and Robinson boundary conditions as a function of time have been applied at the fracture inlet to better represent the field scenario as against the conventional constant source condition (Dirichlet). The model results indicate that there is a difference in concentration between the parallel plate model and random fracture model when it comes to colloidal concentration in the fracture and rock matrix. The variance in concentration is due to the inclusion of variation of the aperture in the variable aperture model, which is absent in the parallel plate model. Additionally, the results suggest that the variable source boundary condition has a significant influence on the transport of colloids in fracture-matrix system. Finally, from the evaluation of the extent of diffusion of colloids into rock matrix, it was concluded that that variable aperture model is associated with more mitigation of colloids compared to the parallel plate model, especially in the case of random fracture.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

Blow-up phenomena for a quasilinear parabolic equation with inner source and nonlinear boundary condition

In this paper, we deal with blow-up phenomena to a quasilinear parabolic equation with inner source and nonlinear boundary condition. By the technique of differential inequality, we establish a lower bound for the blow-up time if blow-up does occur. Furthermore, we consider a specific class of problems to guarantee occurrence of blow-up and derive an upper bound for the blow-up time.

Three-dimensional steady thermodynamic analysis for a double-layer plate with a local heat source and harmonic load

Based on the three-dimensional heat conduction theory, von Karman equation and laminated plate theory, the three-dimensional steady thermodynamic behavior for a double-layer (coating/FGM) plate subjected to a local heat source and harmonic load is investigated in this paper. The exact three-dimensional steady temperature field has been obtained previously by using Poisson method and layer wise method, and then governing equations of the double-layer plate are solved by applying the finite difference method and Newmark method in space domain and time domain, respectively. Numerical results denote that functionally graded index, selected coating layer’s heat conduction coefficient, thickness ratio between total layers and coating layer, width of heat source strip, geometrical condition and boundary condition of the structure have great influence on the deflection and stresses for the double-layer plate.

Analytical solutions of solute transport in a fracture–matrix system with different reaction rates for fracture and matrix

Summary This study deals with the problem of reactive solute transport in a fracture–matrix system using both analytical and numerical modeling methods. The groundwater flow velocity in the fracture is assumed to be high enough (no less than 0.1 m/day) to ensure the advection-dominant transport in the fracture. The problem includes advection along the fracture, transverse diffusion in the matrix, with linear sorption as well as first-order reactions operative in both the fracture and the matrix. A constant-concentration boundary condition and a decay source boundary condition in the fracture are considered. With a constant-concentration source, we obtain closed-form analytical solutions that account for the transport without reaction as well as steady-state solutions with different first-order reactions in the two media. With a decay source, a semi-analytical solution is obtained. The analytical and semi-analytical solutions are in excellent agreement with the numerical simulation results obtained using COMSOL Multiphysics. Sensitivity analysis is conducted to assess the relative importance of matrix diffusion coefficient, fracture aperture, and matrix porosity. We conclude that the first-order reaction as well as the matrix diffusion in the fractured rock would decrease the solute peak concentration and shorten the penetration distance into the fracture. The solutions can be applied to assess the spatial–temporal distribution of concentrations in the fracture and the matrix as well as to assess the contaminant mass stored in the rock matrix. All of these are useful for designing remediation plans for contaminated fractured rocks or for risk assessment of contaminated fracture–matrix systems.

Machine-learning models for the prediction of long-range outdoor sound propagation

Long-range outdoor sound propagation is characterized by a large variance in sound pressure levels due to factors such as refractive gradients, turbulence, and topographic variations. While conventional numerical methods for long-range propagation address these phenomena, they are costly in computational memory and time. In contrast, machine-learning algorithms provide very fast predictions, which this study considers. Observations from either experimental data, or surrogate data from a numerical method, are required for the training of machine-learning models. In this study, a comprehensive training set for the machine learning was created from excess attenuation predictions made with a Crank-Nicholson parabolic equation (CNPE) model. Latin hypercube sampling of the parameter space (source frequency, meteorological factors, boundary conditions, and propagation geometries) generates a set of input for the CNPE model and machine-learning models. Consideration is given to ensemble decision trees, ensemble n...

A Continuous Semianalytic Current Model for DG and NW TFETs

A continuous semianalytic $I$ – $V$ model is developed for double-gate (DG) and nanowire tunnel FETs (TFETs). At the core of the model is a gate-controlled channel potential that satisfies the source and drain boundary conditions. The band-to-band tunneling current is expressed in terms of Franz’s two-band $E(k)$ relation with 3-D density of states. Verified by numerical simulations, the model is capable of generating $I_{\mathrm{ ds}}$ – $V_{\mathrm{ gs}}$ characteristics for any a given bandgap and channel length, based on which the guidelines for TFET scaling are derived. A methodology for evaluating different $I_{\mathrm{\scriptscriptstyle ON}}$ – $I_{\mathrm{\scriptscriptstyle OFF}}$ characteristics, distinguished from the common practice of $I_{\mathrm{\scriptscriptstyle ON}}/I_{\mathrm{\scriptscriptstyle OFF}}$ ratio and SS slope, is employed. Ambipolar effect or channel-to-drain tunneling is also covered by the model. The model has been applied to an example of GaSb–InAs DG TFET, to compare with published atomistic simulation results. $I_{\mathrm{ ds}}$ – $V_{\mathrm{ ds}}$ characteristics are also generated by building into the model the debiasing effect of channel charge in the linear region.

Non-Fourier heat conduction analysis of infinite 2D orthotropic FG hollow cylinders subjected to time-dependent heat source

The non-Fourier heat conduction analysis of infinite 2D functionally graded (FG) hollow cylinders subjected to time-dependent heat source is presented. In this study, a new augmented state space method considering laminate approximation theory is introduced. All material properties are assumed to vary continuously within the cylinder along the specified directions following an arbitrary law. We considered acomplicated heat transfer engineering problem that so far has no analytical and/or numerical solution yet. This problem is solved in the Laplace domain, and to convert the obtained results into the time domain, a numerical Laplace transform inversion with consideration of Gibb's phenomenon is employed. This present method is proposed so general that can solve the heat conduction problems time-dependent heat source and general boundary conditions such as heat flux, convection and combinations of arbitrary temperatures. Eventually, our method is superior in correctness and exactness and also has a sufficient computational cost by comparing the obtained results with some available problems in the literatures.

3DHZETRN: Neutron leakage in finite objects

The 3DHZETRN formalism was recently developed as an extension to HZETRN with an emphasis on 3D corrections for neutrons and light ions. Comparisons to Monte Carlo (MC) simulations were used to verify the 3DHZETRN methodology in slab and spherical geometry, and it was shown that 3DHZETRN agrees with MC codes to the degree that various MC codes agree among themselves. One limitation of such comparisons is that all of the codes (3DHZETRN and three MC codes) utilize different nuclear models/databases; additionally, using a common nuclear model is impractical due to the complexity of the software. It is therefore difficult to ascertain if observed discrepancies are caused by transport code approximations or nuclear model differences. In particular, an important simplification in the 3DHZETRN formalism assumes that neutron production cross sections can be represented as the sum of forward and isotropic components, where the forward component is subsequently solved within the straight-ahead approximation. In the present report, previous transport model results in specific geometries are combined with additional results in related geometries to study neutron leakage using the Webber 1956 solar particle event as a source boundary condition. A ratio is defined to quantify the fractional neutron leakage at a point in a finite object relative to a semi-infinite slab geometry. Using the leakage ratio removes some of the dependence on the magnitude of the neutron production and clarifies the effects of angular scattering and absorption with regard to differences between the models. Discussion is given regarding observed differences between the MC codes and conclusions drawn about the need for further code development. Although the current version of 3DHZETRN is reasonably accurate compared to MC simulations, this study shows that improved leakage estimates can be obtained by replacing the isotropic/straight-ahead approximation with more detailed descriptions.

Modeling of Acoustic Field for a Parametric Focusing Source Using the Spheroidal Beam Equation

Abstract A theoretical model of acoustic field for a parametric focusing source on concave spherical surface is proposed. In this model, the source boundary conditions of the Spheroidal Beam Equation (SBE) for difference frequency wave excitation were studied. Propagation curves and beam patterns for difference frequency component of the acoustic field are compared with those obtained for Khokhlov-Zabolotskaya-Kuznetsov (KZK) model. The results demonstrate that the focused parametric model of SBE is good valid for a large aperture angle in the strongly focused acoustic field. It is also investigated that high directivity and good focal ability with the decreasing of downshift ratio and the increasing of half-aperture angle for the focused parametric model of SBE.

Characterization of medical ultrasound fields using modeling with a boundary condition obtained from measurements

Numerical modeling is becoming an important metrological tool for accurate characterization of ultrasound fields generated by medical transducers in water and in situ. While acoustic propagation equations are well established, setting a boundary condition relevant to the experiment still remains a critical problem. Two methods differing in complexity are described to address this problem. The first method comprises 3D simulations of the Westervelt equation with a boundary condition determined from acoustic holography measurements. The second, simpler method utilizes simulations based either on the KZK or Westervelt equation with an equivalent source boundary condition obtained by matching linear simulations to low-amplitude beam profiles along and transverse to the axis of the source. Calculations with both methods are compared to fiber optic hydrophone measurements of 2D phased therapeutic arrays, a 128-element diagnostic probe, and strongly focused single-element transducers. It is shown that the 3D Westervelt model with holographic boundary condition can accurately simulate the entire nonlinear ultrasound field. The simplified methods based on an equivalent source are shown to give accurate results in the focal zone of the transducers, even when shocks are present in the focal waveform. [Work supported by NIH EB7643, EB016118, DK043881, and RSF 14-12-00974.]

Fracture network optimization for simulating 2D variable-density flow and transport

Numerical simulations in porous media with complex geometries such as fracture networks require irregular meshes with a large number of nodes. Discrete fracture models solve the flow and transport equations with the common node approach. These equations are usually solved simultaneously using common nodes, which increases the computational time as the number of nodes increases. Moreover, the mesh element size at fracture-matrix interfaces need to be further refined, increasing the total number of nodes and computational cost. The main objective of this paper is to efficiently model fracture networks. Therefore we: (i) modify a mesh generator algorithm to generate high-quality meshes for fracture networks where mesh refinement close to the fractures is allowed and (ii) investigate the possibility of reducing the required simulation time by reducing the number of total nodes by removing some fractures from a fracture network. Using a two-dimensional simulation domain of a fractured porous medium under saturated conditions with variable-density flow, we consider 3 statistically equivalent fracture networks embedded in a porous medium containing 50 fractures each with constant aperture. A simplified fracture network is obtained by finding the shortest path in each cluster between the 1st type boundary condition for transport and minimum points in each cluster, where a cluster is defined as all interconnected fractures with at least one fracture intersecting the contaminant source boundary condition. We compare results in terms of penetration depth of the 0.50 isochlore and the contaminant mass. This simplification strategy reduces computational times by up to 36%, while keeping the generated error below 20% both for the penetration depth of the 0.50 isochlore and for the contaminant mass. A sensitivity analysis is performed whereby the free diffusion coefficient, the matrix freshwater permeability, the porosity and the maximum density are modified. Based on these results, the proposed simplification strategy can estimate the penetration depth and the solute mass inside the domain for a wide range of parameter values, saving up to 58% of the CPU time.

An approach for complete 2-D analytical potential modelling of fully depleted symmetric double gate junction less transistor

A novel 2-D analytical potential model of source and drain region along with channel for a fully depleted symmetric double gate junction less transistor is presented in this paper. The boundary conditions for channel potential along the channel length is taken considering source and drain region and boundary conditions for source and drain potential model are derived from channel longitudinal potential expression. The potential model is validated using TCAD simulations. A method for scale length determination is also presented. Scale length expression is obtained from the transverse electrostatic potential expression. Scale length variation with silicon layer thickness and gate oxide thickness is shown. The dependence of Scale length on the dielectric constant is also shown for the three dielectrics--"$$\hbox {SiO}_2 $$SiO2", "$$\hbox {Al}_2 \hbox {O}_3 $$Al2O3" and "$$\hbox {HfO}_2 $$HfO2".