Finite Difference Method For Computation Research Articles

Stretched grid finite difference method for computation of electric field in composite insulators with defects

A 2-dimensional stretched grid finite difference method for the calculation of electric field in composite insulators for up to 1000 kV is presented in this paper. This method is shown to be applicable for composite insulators with and without defects where the inherent axial symmetry cannot be used to simplify the modeling process. This method was initially used to evaluate healthy composite insulators of single and double strings with and without corona and grading rings. Further, a conducting defect was simulated at the high voltage electrode to evaluate 69 and 138 kV insulators. The electric field was also computed using a package based on boundary element method. The accuracy and computational time for all the cases were compared. It has been shown that the proposed method can yield fairly accurate results when compared to other methods, but in a significantly reduced time taken by the latter. The electric field computed for 69 kV composite insulator with defect was compared with the actual measurements using an electro-optic probe. The results show a good agreement. Stretched grid method promises to be an efficient way of quickly computing electric field and this paper quantifies the information obtained for insulators with wide range of system voltages.

Focused ultrasound ablation of solid tumors: Feasibility of planning tissue-selective treatments.

e15600 Background: Focused ultrasound (FUS) is a noninvasive, nonionizing, repeatable local ablative therapy that induces mechanical fractionation or thermal necrosis of a variety of solid tumors including hepatocellular carcinoma, prostate cancer, and desmoid fibromatosis. Recent feasibility studies in animal models have demonstrated the possibility of designing focused ultrasound treatments that are selective (e.g. spare healthy tissue, nerves, and blood vessels) due to differences in tissue and tumor mechanical properties. Given wide variation in individual tumor and patient characteristics, mechanics-based predictions of ablation zone features in different tissues under a range of FUS device settings are needed to permit personalized treatment planning. Methods: A finite difference computational method is used to simulate FUS ablation of tissues with variable mechanical properties (shear moduli of 0.6 – 200 kPa) under different FUS sonication parameters (frequency and peak pressure). The model calculates strain fields contributing to tissue ablation in FUS treatments which are used to predict ablation zone radii and boundary characteristics. Simulation predictions in model tissues are then compared to histology obtained from FUS-treated porcine tissue samples with similar mechanical properties. Results: The mechanical properties of model tissues and FUS treatment parameters have distinct effects on predicted minimum ablation zone radii. For example, smaller ablation zone radii are achieved in stiffer vessel wall than liver under given FUS sonication parameters. In each tissue, lower frequency and higher peak pressure FUS sonication predict a larger ablation zone. Combined variation of sonication frequency and peak pressure are found to achieve wider variation in ablation zone radius than previously achieved with frequency variation alone. Predicted ablation zone radii and boundary characteristics are consistent with the observed histology of FUS-treated tissues. Conclusions: Results show that simulations accounting for tissue mechanical properties and device settings can predict tissue selectivity and ablation zone characteristics observed in FUS procedures. This study demonstrates the potential of using noninvasive measurements of tissue and tumor properties obtained, for example, via shear wave elastography, in combination with micromechanical tissue ablation simulations to develop personalized, selective focused ultrasound treatments for solid tumors.

ТЕПЛОПЕРЕНОС В ГРУНТОВЫХ ОСНОВАНИЯХ ЗДАНИЙ. ВЛИЯНИЕ УТЕПЛЕННОЙ ОТМОСТКИ

In low-rise construction, heat losses to soil foundations are of great importance in the heat balance. For a number of technical reasons, this subject is not well understood. The paper proposes a physical-mathematical and numerical method for calculating unsteady heat transfer, which takes into account outside temperature year changing. A model for calculating heat losses in groundwater is proposed. The numerical model is based on the use of an explicit two-step-in-time, highly stable finite difference computational method. The objects of the study are unheated and heated building with a foundation like a slab on the ground. The effect of insulated blind area on the temperature field under the building and heat loss to the ground is considered. The role of thermal resistance of the blind area and its geometric size is shown.

Finite Difference Computational Method for Trajectory Controllability of a Delayed Damped System Governed by Fractional Differential Equation

In this paper, the trajectory controllability (T-controllability) of a nonlinear fractional-order damped system with time delay is studied. Existence and uniqueness of solution are obtained by using the Banach fixed point theorem and Green's function. Necessary and sufficient conditions of trajectory controllable for the nonlinear system are formulated and proved under a predefined trajectory. Modified fractional finite difference method is applied to the system for numerical approximation of its solution. The applicability of this technique is demonstrated by numerical simulation of two scientific models such as neuromechanical interaction in human snoring and fractional delayed damped Mathieu equation.

Performance Assessment of NAMI DANCE in Tsunami Evolution and Currents Using a Benchmark Problem

Numerical modeling of tsunami evolution, propagation, and inundation is complicated due to numerous parameters involved in the phenomenon. It is important to assess the performance of numerical codes that solve tsunami motion, as well as flow and velocity patterns. NAMI DANCE is a computational tool developed for the modeling of long waves. It provides numerical modeling and efficient visualization of tsunami generation, propagation, and inundation mechanisms and computes the tsunami parameters. In the theory of long waves, the vertical motion of water particles has no effect on the pressure distribution. Based upon this approximation and neglecting vertical acceleration, the equations of mass conservation and momentum are reduced to two-dimensional depth-averaged equations. NAMI DANCE uses finite difference computational method to solve linear and nonlinear forms of depth-averaged shallow water equations in long wave problems. In this study, NAMI DANCE is applied to a benchmark problem which was discussed in the 2015 National Tsunami Hazard Mitigation Program (NTHMP) annual meeting in Portland, USA. The benchmark problem features a series of experiments in which a single solitary wave propagates up a triangular shaped shelf which has an offshore island feature. The problem provides detailed free surface elevation and velocity time series in the vicinity of the island. The comparison of the results showed that NAMI DANCE is able to satisfactorily predict long wave evolution, propagation, amplification, and tsunami currents.

Finite-difference Solution Using Displacement Potential Function for Plane Stresses and Displacements

Abstract This paper presents a finite-difference computational method, which describes the plane state of displacement or stress of the anisotropic materials. The formulas can be used for homogenous domains, but domains with two or more constituent materials (composite materials) can also be modeled and have also solutions, if the equations are written separately for each material's domain, stipulating the condition that on the grid-points of the common boundary the displacement and the stress is equal.

Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference scheme with Computation of a Sonic Injector in Supersonic Cross Flow

AbstractA hybridization of a high order WENO-Zfinite difference scheme and a high order central finite difference method for computation of the two-dimensional Euler equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)] is extended to three-dimensions and for parallel computation. The Hybrid scheme switches dynamically from a WENO-Zscheme to a central scheme at any grid location and time instance if the flow is sufficiently smooth and vice versa if the flow is exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by a high order multi-resolution analysis. The method is tested on a benchmark sonic flow injection in supersonic cross flow. Increase of the order of the method reduces the numerical dissipation of the underlying schemes, which is shown to improve the resolution of small dynamic vortical scales. Shocks are captured sharply in an essentially non-oscillatory manner via the high order shock-capturing WENO-Zscheme. Computations of the injector flow with a WENO-Zscheme only and with the Hybrid scheme are in very close agreement. Thirty percent of grid points require a computationally expensive WENO-Zscheme for high-resolution capturing of shocks, whereas the remainder of grid points may be solved with the computationally more affordable central scheme. The computational cost of the Hybrid scheme can be up to a factor of one and a half lower as compared to computations with a WENO-Zscheme only for the sonic injector benchmark.

Finite-difference method for computation of 3-D gas dynamics equations with artificial viscosity

A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O(τ2 + hx2 + hy2 + hz2) in the areas of the solution’s smoothness and beyond the compression waves; τ is the time step; and hx, hy, and hz are space variable steps. In the proposed difference scheme, in addition to Lax-Wendroff corrections, artificial viscosity μ that monotonizes the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of the computation of the 3D test problem for the Euler equation are presented.

Finite Difference Method for Computation of 1D Pollutant Migration through Saturated Homogeneous Soil Media

The physical processes such as advection, dispersion, and diffusion and interaction between the solution and the soil solids such as sorption, biodegradation, and retention processes have been considered in the governing equation used in the present study. Finite difference method has been adopted herein to solve the one-dimensional contaminant transport model to predict the pollutant migration through soil in waste landfill. In the finite difference technique, the velocity field is first determined within a hydrologic system, and these velocities are then used to calculate the rate of contaminant migration by solving the governing equation. A total of seven contaminants have been chosen for analysis to represent a wide variety of wastes both organic and inorganic. A computer software CONTAMINATE has been developed for solution of the contaminant transport model. Results of this study have been compared with existing analytical solution for validation of the proposed solution technique. Design charts for ...

Review of Computational Aeroacoustics Algorithms

This paper presents a review of recent advancements in computational methodology for aeroacoustics problems. High-order finite difference methods for computation of linear and nonlinear acoustic waves are the primary focus of the review. Schemes for numerical simulation of linear waves include explicit optimized and DRP finite-difference operators, compact schemes, wavenumber extended upwind schemes and leapfrog-like algorithms. Both spatial approximations and time-integration techniques, which include low-dissipation low-dispersion Adams-Bashforth and Runge-Kutta (RK) methods, are examined. Wave propagation properties are analysed in the wavenumber and frequency space. Different approaches to eliminate short-wave spurious numerical waves are also reviewed. Methods for simulating nonlinear acoustic phenomena include essentially non-oscillatory (ENO) schemes, numerical adaptive filtering for high-order explicit and compact finite-difference operators, MacCormack and adaptive compact nonlinear algorithms. A literature survey of other CAA methods is provided in the introductory part.

Pulsed-Laser Ultrasound Generation in Graphite/Epoxy Plate

A laser-based ultrasonic technique using a pulsed laser to stimulate ultrasonic waves in fiber-reinforced graphite/epoxy composite plate is the subject of investigation. For convenience, the material is chosen to be homogeneous and transversely isotropic. The study is strictly limited to the laser power regimes that are suitable for nondestructive evaluation. An elastodynamic methodology is presented based on an integral formulation in order to develop a representation for the dynamic responses in terms of the characteristics of the source that originated the motion. This requires the computation of the elastodynamic Green's function which represents the displacement field from the idealized synthetic sources localized precisely in both space and time. A two-dimensional numerical analysis utilizing a finite difference method for computation of the Green function in a finite plate is developed which provides the basis for quantitative nondestructive evaluation of fiber-reinforced composite materials. Numerical results are presented for the surface displacement at the epicenter. Prediction based on numerical simulations are compared with experimental results.

Finite Difference Methods for Computation of Flow into Local Exhaust Hoods

Local exhaust hoods play an important role in controlling exposures. Airflow into these hoods may be approximated by Laplace's equation. Previous experimental work by other authors along with other data tend to support this assumption. Currently, theoretical models are available for computing the flow into plain and flanged slots and flanged rectangles and circles. These models are analytical solutions of Laplace's equation and are possible because the velocity potentials at a given point in space can be calculated. As the geometry of configurations under study becomes more complex, closed-form solutions to Laplace's equation become more difficult to find. In such situations numerical methods of solution are called for. A finite difference method for computing the airflow is presented and was developed using the plain and flanged slot configurations. The method generally is useful for solving problems in which the location and shape of the flow boundary and the values of the velocity potential or its norm...

Finite Difference Methods for Computation of Flow into Local Exhaust Hoods

Local exhaust hoods play an important role in controlling exposures. Airflow into these hoods may be approximated by Laplace's equation. Previous experimental work by other authors along with other data tend to support this assumption. Currently, theoretical models are available for computing the flow into plain and flanged slots and flanged rectangles and circles. These models are analytical solutions of Laplace's equation and are possible because the velocity potentials at a given point in space can be calculated. As the geometry of configurations under study becomes more complex, closed-form solutions to Laplace's equation become more difficult to find. In such situations numerical methods of solution are called for. A finite difference method for computing the airflow is presented and was developed using the plain and flanged slot configurations. The method generally is useful for solving problems in which the location and shape of the flow boundary and the values of the velocity potential or its normal derivative are known. The analytical models for the slot were used to determine the accuracy of the numerical methods by comparison of the equal velocity contours generated by the various models. Good general agreement between the numerical solutions and analytical models was observed.