Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.

Study of discrete test filters and finite difference approximations for the dynamic subgrid‐scale stress model

Abstract: This paper investigates the effects of discrete test filters and finite‐difference approximations for large‐eddy simulations using the dynamic subgrid‐scale stress model. Discrete explicit test filters based on finite‐difference formulations have been constructed and the characteristics of their transfer function are studied. Several definitions of the scaling factor are investigated in the context of the discrete test filters. Two test filters, one based on a discrete representation of the top‐hat filter (A), and another based on a high‐order filtering operation (C) are evaluated in simulations of the turbulent channel flow at Reτ=180. It is found that filter A calculates a higher turbulent viscosity than filter C, which behaves more like a cutoff filter. For the same test filtering operation, the results are found to be sensitive to the ratio of the characteristic lengths of the test and grid filters. By testing two approximations to the convection terms based on second‐order central difference and a nonconservative fifth‐order upwind biased scheme, it is found that the dynamic procedure is receptive to the difference between the two approximations and adjusts the dynamic constant accordingly. It is found that the dynamic subgrid‐scale stress model is more compatible with the Harlow–Welch scheme than dissipative schemes such as the fifth‐order upwind biased approximation.

Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation

Abstract: Artificial dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained. Both conservative and non-conservative approximations are considered. The dissipation terms are computed such that there is no loss of accuracy

Finite element techniques for modeling groundwater flow in fractured aquifers

Abstract: A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual-porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual-porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one-dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element-convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture-matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.