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 article, a local level set algorithm for simulating interfacial flows described by the two-dimensional incompressible Navier-Stokes equations is presented, which is solved using a finite-difference discretization on a Cartesian grid and a second-order approximate projection method.
Abstract: A local level set algorithm for simulating interfacial flows described by the two-dimensional incompressible Navier–Stokes equations is presented. The governing equations are solved using a finite-difference discretization on a Cartesian grid and a second-order approximate projection method. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid, which is reconstructed every time step and refined using a simple uniform cell-splitting operation within the band. Instabilities at the border of the narrow band are avoided by smoothing the level set function in the outer part of the band. The influence of different PDE-based reinitialization strategies on the accuracy of the results is investigated. The ability of the proposed method to accurately compute interfacial flows is discussed using different tests, namely the advection of a circle of fluid in two different time-reversed vortex flows, the advection of Zalesak's rotating disk, the propagation of small-amplitude gravity and capillary waves at the interface between two superposed viscous fluids in deep water, and a classical test of Rayleigh–Taylor instability with and without surface tension effects. The interface location error and area loss for some of the results obtained are compared with those of a recent particle level set method. Copyright © 2005 John Wiley & Sons, Ltd.
81 citations
TL;DR: In this article, a finite difference method is proposed to remove the need for staggered grids in fluid dynamic computations, which can be applied to free convection in a square cavity, one-dimensional flow through an actuator disk and plane stagnation flow.
Abstract: A new finite difference method, which removes the need for staggered grids in fluid dynamic computations, is presented. Pressure checkerboarding is prevented through a differencing scheme that incorporates the influence of pressure on velocity gradients. The method is implemented in a SIMPLE-type algorithm, and applied to three test problems: one-dimensional flow through an actuator disk, plane stagnation flow, and free convection in a square cavity. Good agreement is obtained between the numerical solutions and the corresponding analytical or benchmark solutions
81 citations
TL;DR: In this article, two diffusional models were developed for finite cylindrical shaped bodies which take into account that mass transfer could have a nonisotropic nature, and applied to the simulation of drying curves of green beans (Phaseolus vulgaris).
Abstract: Two diffusional models were developed for finite cylindrical shaped bodies which take into account that mass transfer could have a nonisotropic nature. In the first model, sample shrinkage was ignored; thus, it was solved by the separation of variables method. This hypothesis of constant sample volume was not assumed in the second model, which solved mass transfer equations through a finite difference scheme. The proposed models were applied to the simulation of drying curves of green beans (Phaseolus vulgaris). Two different effective diffusivity coefficients, one radial and the other axial, as a consequence of the mass transfer through both directions, were estimated in each model. The effective diffusivities estimated with the proposed models varied with the temperature according to the Arrhenius law. The average percentage of variance explained by the fixed boundaries model was 96.1% and increased to 99.1% when shrinkage was considered (in the model solved by a finite difference method). Keywords: Dry...
81 citations
TL;DR: In this paper, a finite differences (FD) solution method is proposed for the numerical treatment of the dynamic equilibrium problem of 2D catenary risers, which is based on the so-called Box approximation, which in the scope of the present contribution is applied to the complete nonlinear model as well as to the reduced linearized formulation.
81 citations
TL;DR: In this article, a numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effects of viscous and Darcy dissipations.
Abstract: A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman- Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal- isothermal, isoflux-isothermal and isothermal-isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell-Over-Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Gras- hof number and Reynolds number for equal and different wall temperatures. Nusselt num- ber at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it coun- ters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model.
81 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |