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, a 3D cascaded lattice Boltzmann method is implemented to simulate the liquid-vapor phase-change process, which is applicable for both the isothermal multiphase flow and the liquid vapor phase change process.
Abstract: In this paper, a three-dimensional (3D) cascaded lattice Boltzmann method (CLBM) is implemented to simulate the liquid–vapor phase-change process. The multiphase flow field is solved by incorporating the pseudopotential multiphase model into an improved CLBM, the temperature field is solved by the finite difference method, and the two fields are coupled via a non-ideal equation of state. Through numerical simulations of several canonical problems, it is verified that the proposed phase-change CLBM is applicable for both the isothermal multiphase flow and the liquid–vapor phase-change process. Using the developed method, a complete 3D pool boiling process with up to hundreds of spontaneously generated bubbles is simulated, faithfully reproducing the nucleate boiling, transition boiling, and film boiling regimes. It is shown that the critical heat flux predicted by the 3D simulations agrees better with the established theories and correlation equations than that obtained by two-dimensional simulations. Furthermore, it is found that with the increase in the wall superheats, the bubble footprint area distribution changes from an exponential distribution to a power-law distribution, in agreement with experimental observations. In addition, insights into the instantaneous and time-averaged characteristics of the first two largest bubble footprints are obtained.
79 citations
TL;DR: In this paper, the temperature distribution and ampacity in a multilayered soil surrounding a system of three cables are calculated in the steady state and in emergency situations, and the finite difference method is used to solve the equations.
Abstract: The temperature distribution and ampacity in a multilayered soil surrounding a system of three cables are calculated in the steady state and in emergency situations. In this paper, we present the mathematical model, which solves the heat diffusion equation in cylindrical coordinates inside the cables and in Cartesian coordinates in the surrounding soil. The finite difference method is used to solve the equations. In order to reduce the number of points studied that are of no interest to the results, a variable step discretization is used. Here, we present the development of the model and the effect of some of the parameters which influence the convergence and accuracy of the method. The application of the model in different configurations and situations is given in the second part of this work, sent for publication at the same time. The model is applicable to the study of buried cables in both the steady state and transient states for short-circuit and overload situations.
79 citations
TL;DR: In this paper, the second-order extension of the Godunov method was used for the solution of two-dimensional Euler equations in the subsonic, transonic, and supersonic flow regimes.
Abstract: The Godunov method and a new second-order accurate extension of the method are used for the solution of two-dimensional Euler equations. Both numerical schemes are described in detail. Their performances in the subsonic, transonic, and supersonic flow regimes are first tested on the problem of flow in a channel with a circular arc bump. The niethods are then applied to calculate the transonic flow through a supercritical com pressor cascade designed by J. Sanzo For this case, the solution with the second-order extension of the Godunov method gives verygood agreement with the design distribution of parameters given by Sanzo
79 citations
TL;DR: In this article, a finite difference method is used to solve the equations governing the conservation of mass, momentum and energy in vapor and liquid phases, and a level set formulation is modified to include the effect of phase change at the liquid-vapor interface and to treat the no-slip condition at the fluid solid interface.
79 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |