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 high-order numerical method was proposed for large-eddy simulations, particularly those containing wall-bounded regions which are considered on stretched curvilinear meshes, where spatial derivatives are represented by a sixth-order compact approximation that is used in conjunction with a tenth-order non-dispersive filter.
Abstract: This work investigates a high-order numerical method which is suitable for performing large-eddy simulations, particularly those containing wall-bounded regions which are considered on stretched curvilinear meshes. Spatial derivatives are represented by a sixth-order compact approximation that is used in conjunction with a tenth-order non-dispersive filter. The scheme employs a time-implicit approximately factored finite-difference algorithm, and applies Newton-like subiterations to achieve second-order temporal and sixth-order spatial accuracy. Both the Smagorinsky and dynamic subgrid-scale stress models are incorporated in the computations, and are used for comparison along with simulations where no model is employed. Details of the method are summarized, and a series of classic validating computations are performed. These include the decay of compressible isotropic turbulence, turbulent channel flow, and the subsonic flow past a circular cylinder. For each of these cases, it was found that the method was robust and provided an accurate means of describing the flowfield, based upon comparisons with previous existing numerical results and experimental data. Published in 2003 by John Wiley & Sons, Ltd.
174 citations
TL;DR: In this paper, an implicit method for the computation of unsteady flows on unstructured grids is presented following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure.
173 citations
TL;DR: In this article, Boussinesq equations describing one-dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub- and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope.
Abstract: Boussinesq equations describing one-dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub- and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope. For this purpose the MacCormack (second-order accurate in space and time) and two-four (second-order accurate in-time and fourth-order in space) explicit finite-difference schemes are used to solve the governing equations subject to specified end conditions until a steady state is reached. The inclusion of initial and boundary conditions is discussed, and the importance of the Boussinesq terms is investigated. Complete test results for a range of Froude numbers are presented that may be used by other researchers for the verification of mathematical models. A comparison of the computed measured results shows that the agreement between them is satisfactory for the fourth-order finite-difference scheme although the second-order scheme does not accurately predict the location of the jump. These simulations show that the Boussinesq terms have little effect in determining the location of the hydraulic jump.
173 citations
TL;DR: In this paper, volume-averaged equations are developed governing steady, laminar, fully developed, hydromagnetic mixed convection non-Darcian flow of an electrically conducting and heat-generating / absorbing fluid in a channel embedded in a uniform porous medium.
Abstract: Volume-averaged equations are developed governing steady, laminar, fully developed, hydromagnetic mixed convection non-Darcian flow of an electrically conducting and heat-generating / absorbing fluid in a channel embedded in a uniform porous medium. Proper dimensionless parameters are employed for various thermal boundary conditions on the left and right walk of the channel prescribed as isothermal-isothermal, isothermal-iso-flux, and isoflux-isothermal. Analytical expressions for the velocity and temperature profiles in the channel as well as for the mass flow rate, friction factor, and heat carried out by the fluid in the channel are developed for special cases of the problem. Conditions for the occurrence of fluid backflow zones are reported. The fully nonlinear governing equations are solved numerically by an implicit finite difference method. Favorable comparisons with the developed analytical results and previously published work are performed. Graphical results of the closed-form and numer...
172 citations
TL;DR: In this article, a model has been established for deep borehole heat exchanger (DBHE) with coaxial tubes, considering coupled heat transfer in the tubes and surrounding subsurface, and an algorithm for direct solution of resulted algebraic equation set is used so as to achieve very efficient computation.
172 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |