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
1 / 2
Papers
17 Jun 1996
TL;DR: It is shown that, due to its neat-elimination of CPU cost dependence on the number of design variables, the adjoint method is preferred over the direct and finite difference methods for practical single-discipline aerodynamic optimization.
Abstract: A methodology for performing optimization on 2D and 3D unstructured grids based on the Euler equations is presented. The same, low-memory-cost explicit relaxation algorithm is used to resolve the discrete equations which govern the flow, linearized direct and adjoint problems. The analysis schemes, for both 2D and 3D, are high resolution Local-Extremum-Diminishing (LED) schemes and use Roe decomposition for the dissipative fluxes. The local timestepping relaxation scheme is based on a multidimensional equivalent of a TVD CFL-like condition guaranteeing convergence of flow and sensitivity computations to machine accuracy. Mesh movement is performed in such a way that optimization of arbitrary geometries is allowed. Sensitivities based on direct and adjoint methods are validated and sample optimizations are performed: the inverse pressure design of a multielement airfoil in high-lift mode, an infinite-span straight transonic wing and a transonic wing/body configuration. It is shown that, due to its neat-elimination of CPU cost dependence on the number of design variables, the adjoint method is preferred over the direct and finite difference methods for practical single-discipline aerodynamic optimization.
79 citations
Journal Article•
TL;DR: In this article, the numerical treatment of fretting in the interface between a body and a rigid foundation is discussed, starting from a variational formulation of a fretting model given in a framework of continuum thermodynamics, an augmented Lagrangian formulation is derived by introducing finite element discretizations in space and a finite difference discretization in time.
Abstract: The present work concerns the numerical treatment of fretting in the interface between a body and a rigid foundation. Starting from a variational formulation of a fretting model given in a framework of continuum thermodynamics, an augmented Lagrangian formulation is derived by introducing finite element discretizations in space and a finite difference discretization in time. The augmented Lagrangian formulation is implemented and solved by a Newton method for the two-dimensional case.
79 citations
TL;DR: In this article, the particle deposition profile was found to be influenced by the mass transfer (both convective and diffusive mass transfer) of the particles in the bulk liquid and by the deposition rate along the substrate.
Abstract: The focus of this article is the numerical study of particle deposition profiles on a solid substrate during the evaporation of a sessile drop of a colloidal particle suspension. The evaporation flux along the drop interface, the induced fluid dynamics inside the drop, and the particle deposition profile on the solid substrate are solved simultaneously. The governing equations are solved numerically using the Galerkin/finite element method (G/FEM) for discretization of the spatial domain and an adaptive finite difference method for discretization in the time domain. Several particle deposition profiles, such as a ring-shaped deposit and uniform particle distribution, are obtained from the numerical simulations. The particle deposition profile is found to be influenced by the mass transfer (both convective and diffusive mass transfer) of the particles in the bulk liquid and by the deposition rate along the substrate. © 2008 American Institute of Chemical Engineers AIChE J, 2008
79 citations
TL;DR: In this paper, the effects of the various parameters on the convectively cooled or convecively heated plate in the laminar boundary layer are considered, as well as skin friction and the rates of mass and heat transfer.
79 citations
TL;DR: In this paper, an implicit difference approximation for the 2D-TFDE is presented, and stability and convergence of the method are discussed using mathematical induction, and a numerical example is given.
Abstract: Fractional diffusion equations have recently been used to model problems in physics, hydrology, biology and other areas of application. In this paper, we consider a two-dimensional time fractional diffusion equation (2D-TFDE) on a finite domain. An implicit difference approximation for the 2D-TFDE is presented. Stability and convergence of the method are discussed using mathematical induction. Finally, a numerical example is given. The numerical result is in excellent agreement with our theoretical analysis.
79 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |