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 paper, an exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time, where no intermediate time responses are required.
Abstract: Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved.
142 citations
TL;DR: It will be shown that significant economies of execution can be attained if nodes are moved so that they remain concentrated in regions of rapid variation of the flow variables.
142 citations
1 Jan 2003
TL;DR: In this paper, a mathematical model to describe the detailed three-dimensional transient heat transfer process in friction stir welding (FSW) is presented, where the heat input from the tool shoulder is modelled as a frictional heat and the heat from a tool pin is modeled as a uniform volumetric heat generated by the plastic deformation near the pin.
Abstract: A mathematical model to describe the detailed three-dimensional transient heat transfer process in friction stir welding (FSW) is presented. This work is both theoretical and experimental. An explicit central differential scheme is used in solving the control equations, the heat transfer phenomena during the tool penetrating, the welding and the tool-removing periods that are studied dynamically. The heat input from the tool shoulder is modelled as a frictional heat and the heat from the tool pin is modelled as a uniform volumetric heat generated by the plastic deformation near the pin. The temperature variation during the welding is also measured to validate the calculated results. The calculated results are in good agreement with the experimental data.
141 citations
TL;DR: This work proposes a novel and efficient implementation of a second order scheme for the induction equation based on an integral form of the underlying conservation law, and shows that the most aggressive formulations reach the same level of accuracy as the other one at a lower computational cost.
141 citations
TL;DR: In this paper, an adorption system with the temperature wave heat generation is numerically analyzed, using a two-dimensional model which takes into account both heat and mass transfer processes inside the adsorber.
141 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |