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
1 / 2
Papers
TL;DR: In this paper, an algorithm for the numerical modeling of magnetotelluric fields in 2D generally anisotropic block structures is presented, where electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor.
Abstract: SUMMARY An algorithm for the numerical modelling of magnetotelluric fields in 2-D generally anisotropic block structures is presented. Electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor. The problem leads to a coupled system of partial differential equations for the strike-parallel components of the electromagnetic field, Ex and H,. These equations are numerically approximated by the finite-difference (FD) method, making use of the integro-interpolation approach. As the magnetic component H, is constant in the non-conductive air, only equations for the electric mode are approximated within the air layer. The system of linear difference equations, resulting from the FD approximation, can be arranged in such a way that its matrix is symmetric and band-limited, and can be solved, for not too large models, by Gaussian elimination. The algorithm is applied to model situations which demonstrate some non-trivial phenomena caused by electrical anisotropy. In particular, the effect of 2-D anisotropy on the relation between magnetotelluric impedances and induction arrows is studied in detail.
159 citations
TL;DR: Similarity equations governing steady hydromagnetic boundary-layer flow over an accelerating permeable surface in the presence of such effects as thermal radiation, thermal buoyancy, and heat generation or absorption effects are obtained in this article.
159 citations
TL;DR: In this article, a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid was developed for the computation of the non-Newtonian extra-stress components on rigid boundaries.
Abstract: This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.
159 citations
TL;DR: A novel numerical method for a degenerate partial differential equation, called the Black-Scholes equation, governing option pricing, based on a fitted finite volume spatial discretization and an implicit time stepping technique is presented.
Abstract: In this paper we present a novel numerical method for a degenerate partial differential equation, called the Black-Scholes equation, governing option pricing. The method is based on a fitted finite volume spatial discretization and an implicit time stepping technique. To derive the error bounds for the spatial discretization of the method, we formulate it as a Petrov-Galerkin finite element method with each basis function of the trial space being determined by a set of two-point boundary value problems defined on element edges. Stability of the discretization is proved and an error bound for the spatial discretization is established. It is also shown that the system matrix of the discretization is an M-matrix so that the discrete maximum principle is satisfied by the discretization. Numerical experiments are performed to demonstrate the effectiveness of the method.
159 citations
TL;DR: In this paper, the steady-state, hydromagnetic forced convective boundary-layer flow of an incompressible Newtonian, electrically-conducting and heat-generating/absorbing fluid over a non-isothermal wedge in the presence of thermal radiation effects is considered.
Abstract: This work is focused on the steady-state, hydromagnetic forced convective boundary-layer flow of an incompressible Newtonian, electrically-conducting and heat-generating/absorbing fluid over a non-isothermal wedge in the presence of thermal radiation effects. The wedge surface is assumed permeable so as to allow for possible wall suction or injection. Also included in the model are the effects of viscous dissipation, Joule heating and stress work. The governing partial differential equations for this investigation are derived and transformed using a non-similarity transformation. In deriving the governing equations, a temperature-dependent heat source or sink term is employed and the Rossland approximation for the thermal radiation term is assumed to be valid. The obtained non-similar equations are solved numerically by an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work on various special cases of the problem are performed and the results are found to be in excellent agreement. Numerical results for the velocity and temperature profiles for a prescribed magnetic parameter as well as the development of the local skin-friction coefficient and local Nusselt number with the magnetic parameter are presented graphically and discussed. This is done in order to elucidate the influence of the various parameters involved in the problem on the solution.
158 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |