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
Papers
More filters
TL;DR: In this article, the 3D finite difference method is used to simulate borehole wave propagations in an isotropic as well as an anisotropic formation, and the finite difference results agree excellently with the analytic solutions of a point force source in the transversely isropic medium.
Abstract: In this paper the three‐dimensional finite difference method is used to simulate borehole wave propagations in an isotropic as well as an anisotropic formation. The finite difference results agree excellently with the analytic solutions of a point force source in the transversely isotropic medium. The finite difference synthetics are also in very good agreement with the discrete wave‐number solutions for fluid‐filled borehole wave propagation. The finite difference synthetics are compared with ultrasonic lab measurements in a scaled borehole model. The borehole is drilled along the X axis in an orthorhombic phenolite solid. Both monopole and dipole logs agree well. The observations of the shear wave splitting in the dipole logs are confirmed by the finite difference simulations. The 3‐D finite difference method is applied to the fluid‐filled borehole wave propagation in the tilted isotropic formation and in the orthorhombic phenolite formation. In a borehole drilled along the Z axis in a phenolite formati...
93 citations
TL;DR: In this article, a finite difference integration scheme for the non-linear dynamic response of beams is proposed, and the proposed scheme mimics the integration scheme obtained by applying the time discontinuous Galerkin methodology to a single degree of freedom linear oscillator.
93 citations
01 Dec 1991
TL;DR: In this article, a finite-difference time-domain (FD-TD) formulation is described, which is equivalent to the symmetrical condensed node model used in the transmission line matrix (TLM) method.
Abstract: A finite-difference time-domain (FD-TD) formulation is described. It is shown that the finite-difference time-domain formulation is equivalent to the symmetrical condensed node model used in the transmission line matrix (TLM) method. The TLM method can be formulated exactly in a finite-difference form in terms of total field quantities. It is shown that, due to a better field resolution and fulfilment of continuity conditions, the FD-TD formulation or its TLM equivalent model give better convergence and accuracy than the traditional FD-TD method. This is illustrated by numerical results pertaining to a finned waveguide. >
92 citations
TL;DR: In this paper, an efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented, which is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form.
Abstract: An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-accurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results.
92 citations
TL;DR: An algorithm for solving Poisson’s equation and the heat equation on irregular domains in three dimensions that provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.
92 citations