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In this paper, a three-dimensional solution of the steady-state advection-diffusion equation is obtained applying the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT), considering non-local closure for turbulent flow. Two different parameterizations were considering for the countergradient term and different methods of numerical inversion for inverse Laplace transform. The results were compared with the experimental data of Copenhagen experiment by an evaluation of statistical indices to analyse the solution of the equation through the methods of numerical inversion. Differents parameterizations for the vertical turbulent eddy diffusivity and wind profile were utilized. The results show a good agreement with the experiment and the methods of numerical inversion for inverse Laplace transform show same efficacy.

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Lévy processes have become very popular in many applications in finance, physics and beyond. The Student-Lévy process is one interesting special case where increments are heavy-tailed and, for 1-increments, Student t distributed. Although theoretically available, there is a lack of path simulation techniques in the literature due to its complicated form. In this paper we address this issue using series representations with the inverse Lévy measure method and the rejection method and prove upper bounds for the mean squared approximation error. In the numerical section we discuss a numerical inversion scheme to find the inverse Lévy measure efficiently. We extend the existing numerical inverse Lévy measure method to incorporate explosive Lévy tail measures. Monte Carlo studies verify the error bounds and the effectiveness of the simulation routine. As a side result we obtain series representations of the so called inverse gamma subordinator which are used to generate paths in this model. [ABSTRACT FROM AUTHOR]

The paper presents a computationally efficient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of effective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of flexibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are effectively algorithmized. [ABSTRACT FROM AUTHOR]

The threshold pressure gradient (TPG) generally exists in the seepage process of low permeability reservoir. In view of characteristics of low permeability seepage, the mathematical model for the moving boundary of non-Darcy flow was established, and the formula for calculating the moving speed of the boundary was given. The Laplace transform and the infinite series method were used to obtain the model’s general solution, and the Stehfest numerical inversion was conducted. The characteristics of moving boundary problems. the boundary change and propagation were discussed and explained in detail, and the phenomenon of TPG extending outward was explicated. The TPG effects on the bottom pressure and the pressure derivative were calculated, and the Gringarten-Bourdet charts under different conditions were given. The results show that, the low pressure percolation model is significantly different from the Darcy seepage model. For low permeability cases, the pressure drop expands with time and the pressure distribution curve is of compact support. The study on the low permeability problem with moving boundary, considering the influence of the TPG and the moving boundary. provides a theoretical basis for the seepage mechanism and production performance, interpretation and numerical simulation of low permeability oil reservoirs. [ABSTRACT FROM AUTHOR]

This article deals with an inverse problem of determining the diffusion coefficients in 2D fractional diffusion equation with a Dirichlet boundary condition by the final observations at the final time. The forward problem is solved by the alternating direction implicit finite-difference scheme with the discrete of fractional derivative by shift Grünwald formula and a numerical text which is to prove its numerically stability and convergence is given. Furthermore, the homotopy regularization algorithm with the regularization parameter chosen by a Sigmoid-type function is introduced to solve the inversion problem numerically. Numerical inversions both with accurate data and noisy data are carried out for the unknown diffusion coefficients of constant and variable with polynomials, trigonometric and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining diffusion coefficients in 2D space fractional diffusion equation, and the algorithm is also numerically stable for additional date having random noises. [ABSTRACT FROM AUTHOR]

This article deals with an inverse problem of determining the space-dependent diffusion coefficient and the source coefficient simultaneously in the multi-term time fractional diffusion equation (TFDE in short) using measurements at one inner point. From a view point of optimality, solving the inverse problem is transformed to minimize an error functional with the help of the solution operator from the unknown to the additional observation. The solution operator is nonlinear but it is of Lipschitz continuity by which existence of a minimum to the error functional is obtained using Sobolev embedding theorems. The homotopy regularization algorithm is introduced to solve the simultaneous inversion problem based on the minimization problem, and numerical examples are presented. The inversion solutions give good approximations to the exact solutions demonstrating that the homotopy regularization algorithm is efficient for the simultaneous inversion problem arising in the multi-term TFDE. [ABSTRACT FROM PUBLISHER]

This paper deals with an inverse problem of determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation with final observations using the variational adjoint method. Data compatibility for the inverse problem is analyzed by which an admissible set for the unknowns is induced. With the aid of an adjoint problem, a bilinear functional based on the variational identity is set forth with which a norm for the unknown is well-defined under suitable conditions, and then a conditional Lipschitz stability for the inverse problem is established. Furthermore, numerical inversions with random noisy data are performed using the optimal perturbation algorithm, and the inversion solutions give good approximations to the exact solution as the noise level goes to small. [ABSTRACT FROM AUTHOR]

This paper deals with numerical solution for the space-time fractional diffusion equation with variable diffusion coefficient, and numerical inversion for the space-dependent diffusion coefficient by the homotopy regularization algorithm. An equivalent system to the forward problem is deduced by utilizing properties of the fractional derivatives, and an implicit finite difference scheme for solving the forward problem is set forth, and its stability and convergence are proved based on estimation to the spectrum radius of the coefficient matrix. The homotopy regularization algorithm is introduced to solve the inverse problem, and numerical inversions are performed with noisy data. The inversion solutions give good approximations to the exact solution as the noise level goes to small demonstrating a numerical stability of the inverse problem here. [ABSTRACT FROM PUBLISHER]

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.

We present a numerical approximate solution to Sobolev-type differential equation subject to nonlocal initial boundary conditions. A Laplace transform method is described for the solution of considered equation. Following Laplace transform of the original problem, an appropriate method of solving differential equations is used to solve the resultant time-independent modified equation and solution is inverted numerically back into the time domain. Numerical results are provided to show the accuracy of the proposed method.

In this paper, an original approach of derivation of equivalent electrical models for multilayer composite materials is presented. The purpose of the modeling is to approximate a given composite material by an equivalent dielectric slab or by a medium consisting from several dielectric layers. For each layer, an equivalent complex permittivity is set up by an optimization procedure in order to achieve the same values of reflection and transmission coefficients as are the measured values of reflection and transmission coefficients of the original composite material.

• A numerical inversion of the bivariate characteristic function. • Conditional characteristic function. • Random number generation • A bivariate logistic distribution. We propose a numerical algorithm for the inversion of the bivariate characteristic function. This will allow the complex probability distribution specified by the characteristic function to be used in practise. Subsequently, it will be possible to create numerical algorithms for a copula function. We will also propose an algorithm for generating random numbers for the case where the bivariate distribution is specified by its characteristic function. This algorithm will be based on the conditional characteristic function. The concept and application of the algorithms will be illustrated using a version of the bivariate logistic distribution specified by its characteristic function. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method to characterize the topology of a porous medium in terms of the pore-size distribution (PSD). This innovative model is based on the dynamic analysis of the oscillating flow of a Newtonian fluid through the porous sample. It consists in using the hydrodynamic transfer function of the porous material and more particularly its admittance. Indeed, the penetration thickness in each pore is a function of the oscillation frequency of the imposed pressure gradient and the viscosity of the fluid. The capillary bundle model (Carman-Kozeny type) was used. This technique has been successfully tested and validated for many types of pore size distributions. Compared to existing techniques, this original method is typical by its simplicity, non-toxicity, and low cost. • We develop a new method to determine the pore size distribution of a porous medium. • We use the dynamic analysis of the oscillating flow of a Newtonian fluid. • The capillary bundle model usually used leads to a Fredholm equation. • The analytical and numerical solutions of this inverse problem give the unknown pore size distribution. • Presentation of pore size distribution using the cumulative distribution function. [ABSTRACT FROM AUTHOR]

Immiscible water-alternating-gas (WAG) flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency. Nevertheless, considering the complicated phase behavior and various multiphase flow characteristics, gas tends to break through early in production wells in heterogeneous formations because of overriding, fingering, and channeling, which may result in unfavorable recovery performance. On the basis of phase behavior studies, minimum miscibility pressure measurements, and immiscible WAG coreflood experiments, the cubic B-spline model (CBM) was employed to describe the three-phase relative permeability curve. Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially, optimization of production performance including pressure drop, water cut, and the cumulative gas-oil ratio was performed. A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process. Based on the quantitative characterization of major recovery mechanisms, the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment. The proposed method is reliable and can meet engineering requirements. It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve. [ABSTRACT FROM AUTHOR]

The authors formulate the initial-boundary-value problem of step pulse propagating from input to output on the basis of a hyperbolic equation with dissipation, which describes the propagation of waves with a finite speed. Exact analytical solution is obtained in the Laplace transform space. Numerical inversion of the Laplace transform by using Euler's method is carried out and the results are analyzed. [ABSTRACT FROM AUTHOR]

Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated. [ABSTRACT FROM AUTHOR]

This paper considers a k-out-of- n: G repairable system, in which the working times and repair times of components are governed by exponential distributions and general distributions, respectively. Applying the semi-Markov process theory, the Cramer's rule and the Laplace (Laplace-Stieltjes) transform, several important performance measures including the availability, the rate of occurrence of failures, the mean up time and the mean time between failures of the system are derived. Moreover, numerical inversion of Laplace transform is carried out to discuss the time-dependent behavior of system performance measures. In addition, a special case ( n − 1)-out-of- n: G repairable system is presented to verify the correctness of the analytical results. [ABSTRACT FROM AUTHOR]

The model HYDRUS-1D was used to simulate soil water dynamics of full and deficit irrigated maize grown under a rainout shelter during two crop seasons. Four irrigation treatments were established based on the amount of water applied to fulfil crop water requirements. Treatment D1 was irrigated to fully satisfy crop water requirements, while treatments D2 (mild deficit), D3 (moderate deficit), and D4 (severe deficit) were for increased controlled water stress conditions. The computation and partitioning of evapotranspiration data into soil evaporation and crop transpiration was carried out with the SIMDualKc model, and then used with HYDRUS-1D. The soil hydraulic properties were determined from numerical inversion of field water content data. The compensated root water uptake mechanism was used to describe water removal by plants. The HYDRUS-1D model successfully simulated the temporal variability of soil water dynamics in treatments irrigated with full and deficit irrigation, producing RMSE values that varied between 0.014 and 0.025 cm 3 cm −3 when comparing model simulations with field measurements. Actual transpiration varied between 224 and 483 mm. Potential transpiration reductions varied from 0.4 to 48.8% due to water stress, but plants were able to compensate for the water deficits in the surface layers by removing more water from the deeper, less stressed layers. HYDRUS-1D water balance estimates were also comparable with the corresponding ones determined with the SIMDualKc water balance model. Both modelling approaches should contribute to improve the web-based IRRIGA system, used to support farm irrigation scheduling in Brazil. [ABSTRACT FROM AUTHOR]