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: A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation, which is especially suitable for moderate to large Reynolds number flows.
Abstract: A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to large Reynolds number flows. The momentum equation is discretized by a compact fourth order scheme with the no-slip boundary condition enforced using a local vorticity boundary condition. Fourth order long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth order Runge–Kutta. The method is highly efficient. The main computation consists of the solution of two Poisson-like equations at each Runge–Kutta time stage for which standard FFT based fast Poisson solvers are used. An example of Lorenz flow is presented, in which the full fourth order accuracy is checked. The numerical simulation of a strong shear flow induced by a temperature jump, is resolved by two perfectly matching resolutions. Additionally, we present benchmark quality simulations of a differentially-heated cavity problem. This flow was the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001.
89 citations
TL;DR: It is observed that velocity increases with an increase in both micro-polar parameter and thermal buoyancy parameter, and for the temperature profiles opposite behavior is observed for increment in both unsteadiness parameter and Thermal buoyancy parameters.
89 citations
1 Jul 1972
TL;DR: In this paper, Brailovskaya's finite difference method was used to obtain steady-state solutions to the Navier-Stokes equations for a supersonic laminar flow over a two-dimensional compression corner.
Abstract: Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite difference method of Brailovskaya, which has second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and wall pressure distributions measured experimentally for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat plate flow field, beginning at the leading edge. The compression corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points.
89 citations
TL;DR: This paper examines iterative methods for solving the semiconductor device equations using the PISCES-II device simulator as a vehicle and the dependencies of these methods on factors such as choice of variables, bias condition and initial guess are analyzed.
Abstract: This paper examines iterative methods for solving the semiconductor device equations. The emphasis is on fully coupled methods, because of the failure of decoupled methods for on-state devices. Using the PISCES-II device simulator as a vehicle, incomplete factorization and operator decomposition iterative methods are presented for solving the Newton equations. The dependencies of these methods on factors such as choice of variables, bias condition and initial guess are analyzed. The results are compared with sparse Gaussian elimination.
89 citations
TL;DR: A new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order accuracy along all directions, and is more accurate and more stable than the conventional one for the same M.
89 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |