Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this article, the authors present the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation, including the classical MFEM, the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control volume method.
Abstract: This paper presents the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation The methods discussed are the classical mixed finite element method (MFEM), the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control-volume method These methods are all locally mass conservative, and handle general irregular grids with anisotropic and heterogeneous discontinuous permeability In addition to this, the methods have a common weak continuity in the pressure across the edges, which in some cases corresponds to Lagrange multipliers It seems that this last property is an essential common quality for these methods
107 citations
TL;DR: In this article, the authors studied laminar, steady state flow in helically coiled tubes at a constant wall temperature, numerically and experimentally, using a finite difference method with projection algorithm using FORTRAN programming language.
107 citations
TL;DR: In this article, a mathematical model for the blood flow in stenosed artery in the presence of magnetic field is proposed and the laminar, incompressible, fully developed, non-Newtonian flow of blood in an artery having multiple stenosis is numerically studied under the action of transverse magnetic field.
Abstract: In the present study a mathematical model for the blood flow in stenosed artery in the presence of magnetic field is proposed. The laminar, incompressible, fully developed, non-Newtonian flow of blood in an artery having multiple stenosis is numerically studied under the action of transverse magnetic field. The governing equations are transformed by using a radial transformation and the numerical results are obtained using a finite difference technique. Effect of overlapping stenosis and externally applied magnetic field in the blood flow is discussed with the help of graph. All the flow characteristics are found to be affected by the presence of multiple stenosis and exposure of magnetic field of different intensities.
Keywords: Blood flow, Magnetic Field, Overlapping Stenosis, generalized Power Law, Finite Difference Method
107 citations
TL;DR: The semianalytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied in this article.
Abstract: The semianalytical method of design sensitivity analysis that is widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements is studied. It is shown that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Errors are shown to be associated with an incompatibility of the sensitivity field with the structure. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. A method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.
107 citations
TL;DR: In this article, a Fourier series analysis is performed to determine the dissipative and dispersive characteristics of finite difference and finite element methods for solving the convective-dispersive equation.
Abstract: Various finite difference and finite element methods for solving the one-dimensional convective-dispersive equation are investigated. A Fourier series analysis is performed to determine the dissipative and dispersive characteristics of these numerical methods. The analysis indicates that the commonly observed phenomenon of overshoot of a concentration pulse is due to the inability of the numerical schemes to propagate the small wavelengths which are important to the description of the front. Furthermore, the numerical smearing of a sharp front is due to dissipation of these small wavelengths. The finite element method was found to be superior to finite difference methods for solution of the convective-dispersive equation.
107 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |