Analytical Boundary Research Articles

Analysis and modeling of char particle combustion with heat and multicomponent mass transfer

A char combustion model suitable for a large-scale boiler/gasifier simulation, which considers the variation of physical quantities in the radial direction of char particles, is developed and examined. The structural evolution within particles is formulated using the basic concept of the random pore model while simultaneously considering particle shrinkage. To reduce the computational cost, a new approximate analytical boundary condition is applied to the particle surface, which is approximately derived from the Stefan–Maxwell equations. The boundary condition showed reasonably good agreement with direct numerical integration with a fine grid resolution by the finite difference method under arbitrary conditions. The model was applied to combustion in a drop tube furnace and showed qualitatively good agreement with experiments, including for the burnout behavior in the late stages. It is revealed that the profiles of the oxygen mole fraction, conversion, and combustion rate have considerably different characteristics in small and large particles. This means that a model that considers one total conversion for each particle is insufficient to describe the state of particles. Since our char combustion model requires only one fitting parameter, which is determined from information on the internal geometry of char particles, it is useful for performing numerical simulations.

Role of the sample boundaries in the problem of dissipative magnetization dynamics

The Landau–Lifshitz or the Landau–Lifshitz–Gilbert equation of motion for the magnetization M(r,t) a partial integro-differential equation in time and space, for which, in general, an initial value condition and a boundary condition for the field have to be prescribed. This, however, is only true for analytic solutions. It is shown that a unique albeit approximate numerical solution of M(r,t) in a finite sample with surfaces, for which the position dependent form of the effective field occurring in these equations with position dependent material parameters is used, no boundary condition of the magnetization is required. The analytical boundary conditions nevertheless play an important role also in numerical simulations, since they provide valuable estimates required for the accurate calculation of the exchange field at the surfaces.

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

SUMMARYThe accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.

A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide

A problem of a nonconfocal suspended strip in an elliptical waveguide is analyzed by using a semianalytical approach, which is the so-called null-field boundary integral-equation method (BIEM). The null-field BIEM is proposed by introducing the idea of null field, degenerate kernels, and eigenfunction expansion to improve the conventional dual boundary-element method (BEM). A closed-form fundamental solution can be expressed in terms of the degenerate kernel containing the Mathieu and modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. By this way, the efficiency is promoted in three aspects: analytical boundary integral without numerical error, natural bases for boundary densities, and exact description of boundary geometry. Due to the semianalytical formulation, the null-field BIEM can fully capture the property of geometry and the error only occurs from the truncation of the number of the eigenfunction expansion terms in the real implementation. The present method is also a kind of meshless method since only boundary nodes are needed to construct influence matrices instead of using boundary elements. Both TE and TM cases are considered in this paper. To verify the validity of the present method, the dual BEM and finite-element method are also utilized to provide cutoff wavenumbers. Besides, the analytical solution of a confocal elliptical waveguide can be derived by using the present method. After comparing with published data, good agreement is made.

Self-consistent numerical dispersion relation of the ablative Rayleigh-Taylor instability of double ablation fronts in inertial confinement fusion

The linear stability analysis of accelerated double ablation fronts is carried out numerically with a self-consistent approach. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using 1D simulation results. Numerical dispersion relation is compared to an analytical sharp boundary model [Yañez et al., Phys. Plasmas 18, 052701 (2011)] showing an excellent agreement for the radiation dominated regime of very steep ablation fronts, and the stabilization due to smooth profiles. 2D simulations are presented to validate the numerical self-consistent theory.

Recent mechanical weakening of the Arctic sea ice cover as revealed from larger inertial oscillations

We present a simple and analytical ocean boundary layer‐sea ice coupled dynamical model that we apply to the modeling of Arctic sea ice motion in the frequency domain, and particularly in the inertial range. This study further complements our related work in an unpublished paper where the sea ice cover response to the Coriolis forcing has been studied. This analytical model allows interpretation of the spatial, seasonal and pluriannual dependence of the magnitude of the inertial oscillations detailed in terms of mechanical behavior of the ice cover. In this model, the sea ice mechanical response is simplified through the introduction of a linear internal friction term K. A dependence of K allows us to explain the associated dependence of the seasonal and regional Arctic sea ice inertial motion. In addition, a significant decrease of K, i.e., a mechanical weakening of the sea ice cover, is observed for the period 2002–2008 compared to 1979–2001, for the entire Arctic in both seasons. These results show that the regional, seasonal and pluriannual variations of sea ice inertial motion are not only the trivial consequence of simultaneous variations of thickness and concentration (and so of ice mass per unit area). Instead, the shrinking and thinning of the Arctic sea ice cover over the last few decades has induced a mechanical weakening, which in turns has favored sea ice fracturing and deformation.

Stochastic volatility asymptotics of stock loans: Valuation and optimal stopping

A stock loan, or equity security lending service, is a loan which uses stocks as collateral. The borrower has the right to repay the principal with interest and regain the stock, or make no repayment and surrender the stock. Therefore, the valuation of stock loan is an optimal stopping problem related to a perpetual American option with a negative effective interest rate. The negative effective interest rate makes standard techniques for perpetual American option pricing failure. Using a fast mean-reverting stochastic volatility model, we applied a perturbation technique to the free-boundary value problem for the stock loan price. An analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion.

Rigorous evaluation of a soil heat transfer model for mesoscale climate change impact studies

The influence of Climate Change on plant development as well as on carbon and nitrogen cycling in soils is an important research topic for Global Change impact assessment at the regional scale. These changes affect the availability and quality of ground and surface waters and accordingly the future productivity of agriculturally used landscapes. The integrated assessment of these changes requires a robust prediction of the potential future characteristics of soil temperature and moisture based on scale-appropriate, process-oriented models. Hence, we present the Soil Heat Transfer Module (SHTM) used as a component of the mesoscale decision support system DANUBIA, which is developed by the multi-disciplinary research project GLOWA-Danube (www.glowa-danube.de). DANUBIA is applied on the Upper Danube catchment to assess the future changes in water availability, quality and use based on Global Change scenarios.In order to cover the temporal and spatial resolution (1h, 1×1km) of the main model as well as the desired investigation period of 50 years, SHTM combines a variable time step conductive heat transfer algorithm with an analytical lower boundary condition to react to long-term climate change with minimal model drift. Changes in soil moisture and soil freezing are explicitly taken into account. The ground heat flux at the soil surface is computed by iterative closure of the energy balance including radiative, latent and sensible energy fluxes. Validation of the heat transfer scheme shows that the variable time step solution improves computational efficiency while imposing only minimal RMSE and phase shift errors. Furthermore, the analytical lower boundary stabilizes the long term heat balance and induces a rather small potential model drift in the order of 0.001Wm−2. Then the results of the full land surface model including SHTM are compared to measurements at 25 agrometeorological sites. Without site-specific parameterisation other than land cover type, we show that the model performs well (RMSE about 2K) in reproducing daily and annual top soil temperature dynamics over long simulation periods. The analysis of systematic model errors reveals that about 75% of the RMSE is attributable to uncertainties in meteorological input, canopy parameters and snow processes.

An analytical boundary element integral approach to track the boundary of a moving cavity using electrical impedance tomography

This paper is about locating the boundary of a moving cavity within a homogeneous background from the voltage measurements recorded on the outer boundary. An inverse boundary problem of a moving cavity is formulated by considering a two-phase vapor–liquid flow in a pipe. The conductivity of the flow components (vapor and liquid) is assumed to be constant and known a priori while the location and shape of the inclusion (vapor) are the unknowns to be estimated. The forward problem is solved using the boundary element method (BEM) with the integral equations solved analytically. A special situation is considered such that the cavity changes its location and shape during the time taken to acquire a full set of independent measurement data. The boundary of a cavity is assumed to be elliptic and is parameterized with Fourier series. The inverse problem is treated as a state estimation problem with the Fourier coefficients that represent the center and radii of the cavity as the unknowns to be estimated. An extended Kalman filter (EKF) is used as an inverse algorithm to estimate the time varying Fourier coefficients. Numerical experiments are shown to evaluate the performance of the proposed method. Through the results, it can be noticed that the proposed BEM with EKF method is successful in estimating the boundary of a moving cavity.

A Mur Type Analytical Absorbing Boundary Condition for Multidimensional Wave Analysis with the Directional Splitting Technique

A Mur type analytical absorbing boundary condition (A-ABC), which is based on the one-dimensional one-way wave equation, is proposed for multidimensional wave analysis by introducing the directional splitting technique. This new absorbing boundary condition is expansion of the first-order Mur. The absorbing ability, required memory, and calculation speed of the Mur type A-ABC are evaluated by comparison with those of conventional ABCs. The result indicated that absorbing ability of the proposed ABC is higher than the first-order Mur and lower than the second-order Mur at large incident angle. While, our proposed ABC has advantage in both required memory and calculation speed by comparison with the second-order Mur. Thus, effectivity of the proposed Mur type A-ABC is shown.

Three-Dimensional Micrometer-Scale Modeling of Quenching in High-Aspect-Ratio $\hbox{YBa}_{2}\hbox{Cu}_{3}\hbox{O}_{7 - \delta}$ Coated Conductor Tapes—Part I: Model Development and Validation

YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7-δ</sub> coated conductors have very slow normal-zone propagation velocity, which renders quench detection and protection very difficult. To develop effective quench detection methods, it is paramount to study the underlying behavior that drives quench propagation at the micrometer-scale level. Toward this end, numerical mixed-dimensional models, composed of multiple high-aspect-ratio thin layers, are developed. The high-aspect-ratio modeling issues are tackled by approximating the thin layers either as a 2-D surface or as an analytical contact resistance interior boundary condition, which also acts as a coupling bridge between the 2-D and 3-D behaviors. The tape models take into account the thermal and electrical physics of each layer in actual conductor dimensions and are implemented using commercial finite-element analysis software. In the first part of this two-part paper, the mixed-dimensional models are introduced and then computationally and experimentally validated. Validations are gauged by comparisons in normal-zone propagation velocity and in the time-dependent voltage and temperature profiles. Results show that the mixed-dimensional models can not only effectively address the high-aspect-ratio modeling issues of thin films but also accurately and efficiently reproduce physical quench phenomena in a coated conductor.

The enforcement–exploitation trade-off in international cooperation between weak and powerful states

According to the imperative of enforcement, states must threaten defectors with sanctions or reciprocal suspension of international cooperation. I show that in international cooperation between the weak and the powerful, states should nevertheless limit the supply of collective enforcement power. Strong sanctions allow exploitative international agreements, so weak states refuse to engage in negotiations with powerful states in the first place. For powerful states, toothless international agreements are a credible commitment to limit power politics. The result holds even if sanctions can be used only to enforce international agreements and not for coercion. It implies that under power asymmetry, states must accept constraints on the use of power, as opposed to simply maximizing the supply of collective enforcement power. The theory offers a new perspective to international cooperation and a synthesis of the enforcement and managerial schools of international cooperation. It produces precise analytical boundary conditions and generates falsifiable empirical hypotheses.

Hobbes, Holmes, and Dewey: Pragmatism and the Problem of Order

Civil war was a catalyst in forming the jurisprudential views of Thomas Hobbes and Oliver Wendell Holmes Jr. In this paper I claim that Holmes’s pragmatism advances a fundamentally distinct view of order from Hobbes, a dynamic rather than analytical and static conception, which can be seen by comparing their response to perennial conflict, which both made central in all its forms: military, political, moral, and intellectual. The difference is that Hobbes resolved the problem of conflict through authority, while Holmes does so through inquiry and the adjustment of practices. I propose three dimensions in which to elucidate this: historical, ontological, and practical. By historical I mean Holmes’s replacement of the Hobbesian analytical model of law, designed to address (and presumably suppress) conflict by state control, with an endogenous model that assimilates conflict in a process of formal but communal inquiry into discrete types of dispute. By ontological I mean Holmes’s rejection of the analytical boundary around law, dating to Hobbes and still reflected in the contemporary separation of law and morals, in favor of a holistic fallibilism, which like Dewey’s encompasses all inquiry - legal, scientific, ethical, aesthetic, philosophical - under one ontological roof. The third or practical dimension refers to Holmes’s critique of ideology, best known from the words of his famous dissent in Lochner v. New York: “The fourteenth amendment does not enact Mr. Herbert Spencer’s Social Statics”; or, more to the point, “general propositions do not decide concrete cases.”

Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives

Electrical resistance tomography is a novel non-intrusive technique to image the electrical conductivity distribution. The technique is characterized as a nonlinear, ill-posed inverse problem with many unknowns. A numerical method based on boundary element method is presented in this paper, aiming to obtain the boundary of inclusions with a constant conductivity. The forward problem employs the complete electrode model and the size of system matrix is reduced. The Jacobian matrix is established through the partial derivatives of element integrals and linearization of the system. The analytical integrations for quadratic elements are presented, where higher-order integrals are expressed by lower-order ones for rapid calculation. The iterative Levenberg–Marquardt method is adopted to solve the inverse problem.

Solution of Poisson’s equation by analytical boundary element integration

The solution of Poisson’s equation is essential for many branches of science and engineering such as fluid-mechanics, geosciences, and electrostatics. Solution of two-dimensional Poisson’s equations is carried out by BEM based on Galerkin Vector Method in which the integrals that appear in the boundary element method are expressed by analytical integration. In this paper, the Galerkin vector method is developed for more general case than presented in the previous works. The integrals are computed for constant and linear elements in BEM. By employing analytical integration in BEM computation, the numerical schemes and coordinate transformations can be avoided. The presented method can also be used for the multiple domain case. The results of the analytical integration are employed in BEM code and the obtained analytical expression will be applied to several examples where the exact solution exists. The produced results are in good agreement with the exact solution.

Temperature beneath continents as a function of continental cover and convective wavelength

Geodynamic modeling studies have demonstrated that mantle global warming can occur in response to continental aggregation, possibly leading to large‐scale melting and associated continental breakup. Such feedback calls for a recipe describing how continents help to regulate the thermal evolution of the mantle. Here we use spherical mantle convection models with continents to quantify variations in subcontinental temperature as a function of continent size and distribution and convective wavelength. Through comparison to a simple analytical boundary layer model, we show that larger continents beget warming of the underlying mantle, with heating sometimes compounded by the formation of broader convection cells associated with the biggest continents. Our results hold well for purely internally heated and partially core heated models with Rayleigh numbers of 105 to 107 containing continents with sizes ranging from that of Antarctica to Pangea. Results from a time‐dependent model with three mobile continents of various sizes suggests that the tendency for temperatures to rise with continent size persists on average over timescales of billions of years.

Unstructured tetrahedral mesh generation technology

We present a robust unstructured tetrahedral mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh generation technique. For boundary mesh generation we propose four different approaches using analytical boundary parameterization, interface with CAD systems, surface mesh refinement, and constructive solid geometry. These methods allow us to build a flexible grid generation technology with a user friendly interface.

3D ANALYSIS OF RIGHT ANGLE TUNNELS UNDER WAVE PROPAGATION EFFECT WITH BEM

Tunnel is integral part of the infrastructure of modern society and is used for a wide range of applications, including highway, sewage and water transport. This structure built in areas subject to earthquake activity and must withstand safely seismic waves. Seismic waves are characterized in terms of the deformations and strains imposed on the structure by the surrounding ground, often due to the interaction between two. Dynamic analysis of lined tunnel with bending in longitudinal axis is not a common case and is not exist in literature as rich as long lined tunnel with straight axis. In this paper the case was analyzed with BEM in full space time domain. Tunnel with bending in longitudinal axis and large backfilling is dynamically analyzed in three dimensional contexts by assuming linear or viscoelastic material behavior, full contact between soil and structure at their interface without modeling free surface of ground. An analytical boundary integral equation is developed for the efficient time domain dynamic response analysis of a bending cavity with arbitrary cross-section geometry. The numerical solution of boundary integral equation is obtained after discretizing both space and time variation. First curvilinear coordinates, which Z axis is along main longitudinal line, is introduced. Geometry of bend, displacement and traction is expressed in this coordinates. Complex shape of the cross section is mapping into a circular shape with a unit radius by trigonometric shape functions. This mapping enables us to discretize the boundary only along the longitudinal axis of tunnel. Therefore boundary is divided into N circular element this is because of advantages of circular element. Harmonic substantial behavior of deformation and traction, which expressed in cylindrical coordinates, results their variation with central angle expressed in Fourier series. This helps us to decrease the number of equation very much. Observation time is divided into M time step. Appropriate time step is chose because it is very important for numerical stability of transient dynamic problems. Weak and strong singularity occurs during integration process. Direct approach for the rigorous treatment and numerical evaluation is used. For this purpose circular element divided into subdivision elements and integration is done in each element. Singular points exist in one subdivision. Polar coordinates and CPV sense is used for evaluating strong singularity and three coordinates transformation is used for eliminating weak singularity. After all, equation should be solved for the total displacement and tractions at inner and outer surface of tunnel. This is accomplished by especial out of core block equation solver of gauss type for non-symmetric matrices. Numerical results are presented for the case of lined curve tunnel of circular cross section with some values in bending radius, tunnel radius and thickness of tunnel. Plain strain theory results are compared with the straight portion of the model.

Exact solution for orthotropic materials weakened by doubly periodic cracks of unequal size under antiplane shear

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.

Computation of 3-D Sensitivity Coefficients in Magnetic Induction Tomography Using Boundary Integral Equations and Radial Basis Functions

This paper presents a method for the numerical computation of 3-D sensitivity coefficients of a target object in magnetic induction tomography (MIT). The sensitivity coefficient at a point is defined as the dot product of electromagnetic fields produced by unit current flowing in the excitation and the detector coil. In this paper, the fields are governed by a set of boundary integral equations (BIEs). Numerical results demonstrate that the fields on the boundary and interior volume domain of the target can be accurately represented by radial basis functions (RBFs). The paper compares numerical solutions of the BIEs based on RBFs with analytical solutions and boundary element solutions.