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: This paper describes the numerical techniques used to solve the coupled system of nonlinear partial differential equations which model semiconductor devices, and the efficient solution of the resulting nonlinear and linear algebraic equations.
Abstract: This paper describes the numerical techniques used to solve the coupled system of nonlinear partial differential equations which model semiconductor devices. These methods have been encoded into our device simulation package which has successfully simulated complex devices in two and three space dimensions. We focus our discussion on nonlinear operator iteration, discretization and scaling procedures, and the efficient solution of the resulting nonlinear and linear algebraic equations. Our companion paper [13] discusses physical aspects of the model equations and presents results from several actual device simulations.
293 citations
TL;DR: In this article, the effects of the viscosity/temperature parameter G r the thermal-diffusion parameter Sr (Soret number) and the diffusion-thermo parameter Df (Dufour number) have been examined on the flow field of a hydrogen-air mixture as a non-chemical reacting fluid pair.
293 citations
TL;DR: A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom, and it is shown to provide convergent solutions over the full physical and discrete parameter space of interest.
292 citations
TL;DR: The new method, unlike the older approaches, yields optimal estimates for the primal variable in both the element size h and polynomial degree p, and outperforms the standard upwind DG method.
291 citations
TL;DR: MacCormack and Gabutti as mentioned in this paper introduced explicit finite-difference schemes to integrate the equations describing two-dimensional, unsteady gradually varied flows, which allow sharp discontinuous initial conditions, and do not require isolation of the bores.
Abstract: MacCormack and Gabutti explicit finite‐difference schemes are introduced to integrate the equations describing two‐dimensional, unsteady gradually varied flows. Both schemes are second‐order accurate in space and time, allow sharp discontinuous initial conditions, and do not require isolation of the bores. Both sub‐ and supercritical flows may be present simultaneously in different parts of the channel or in a sequence in time. The inclusion of boundaries and stability conditions and the addition of artificial viscosity to smooth high‐frequency oscillations are discussed. To illustrate application of the schemes in hydraulic engineering, two typical problems are solved and the results of different schemes are compared.
291 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |