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
TL;DR: In this article, a finite-difference method for reservoir simulation with flexible approximation of reservoir geometry and reduced grid-orientation effects is presented. But the method is not suitable for the case of irregular or locally irregular grids.
Abstract: This paper describes a practical method in which irregular or locally irregular grids are used in reservoir simulation with the advantages of flexible approximation of reservoir geometry and reduced grid-orientation effects. Finite-difference equations are derived from an integral formulation of the reservoir model equations equivalent to the commonly used differential equations. Integrating over gridblocks results in material-balance equations for each block. This leads to a finite-volume method that combines the advantages of finite-element methods (flexible grids) with those of finite-difference methods (intuitive interpretation of flow terms). Grid-orientation effects are investigated. For grids based on triangular elements, the more isotropic distribution of gridpoints diminishes the orientation effect significantly. Numerical examples show that the regions of interest in a reservoir can be simulated efficiently and that well flow can be represented accurately.
170 citations
TL;DR: This work develops a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations, based on adaptive-order finite difference methods and spectral methods.
Abstract: Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity $\mathrm{poly}(1/\epsilon)$, where $\epsilon$ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be $\mathrm{poly}(d, \log(1/\epsilon))$, where $d$ is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.
169 citations
TL;DR: An efficient local mesh refinement algorithm, subdividing a computational domain to resolve fine dimensions in a time-domain-finite-difference (TD-FD) space-time grid structure, is discussed in this paper.
Abstract: An efficient local mesh refinement algorithm, subdividing a computational domain to resolve fine dimensions in a time-domain-finite-difference (TD-FD) space-time grid structure, is discussed. At a discontinuous coarse-fine mesh interface, the boundary conditions for the tangential and normal field components are enforced for a smooth transition of highly nonuniform held quantities. >
168 citations
TL;DR: Why and how the discontinuous Galerkin (DG) formulation can be used for under-resolved turbulence simulations without explicit subgrid-scale modelling is clarified and the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power.
168 citations
TL;DR: In this paper, a finite difference method is extended to high Reynolds number flow about circular cylinders with particular emphasis given to the quantitative description of fine flow features, and a cell structure is chosen which provides local cell dimensions consistent with the structure of solutions expected.
Abstract: A finite difference method is extended to high Reynolds number flow about circular cylinders with particular emphasis given to the quantitative description of fine flow features. The method is of the explicit type and includes a directional difference scheme for the nonlinear terms which enhances calculational stability at high Reynolds numbers. A cell structure is chosen which provides local cell dimensions consistent with the structure of solutions expected. Solutions are presented for a range of Reynolds numbers from 1 to 3 × 105 in which the flow is started impulsively from rest, and the development is studied up to the approach of the steady‐state or the limit cycle condition, whichever is appropriate to the particular Reynolds number.
168 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |