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.
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TL;DR: Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.
197 citations
TL;DR: General results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi- Bellman equations with variable coecients are obtained using systematically a tricky idea of N.V. Krylov.
Abstract: Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference schemes in the stationary case with constant coefficients and in the time-dependent case with variable coefficients by using control theory and probabilistic methods. In this paper we are able to handle variable coefficients by a purely analytical method. In our opinion this way is far simpler and, for the cases we can treat, it yields a better rate of convergence than Krylov obtains in the variable coefficients case.
197 citations
TL;DR: In this article, the two dimensional MHD flow of Eyring-Powell fluid model towards a stretching sheet was examined and it was found that the increase in the intensity of the magnetic field as well as Eyring and Powell fluid parameter γ shows resistance to the flow.
197 citations
TL;DR: In this paper, a time domain numerical model based on the fully nonlinear extended Boussinesq equations was used to investigate surface wave transformation and breaking-induced nearshore circulation.
Abstract: In this study, we use a time domain numerical model based on the fully nonlinear extended Boussinesq equations [Wei et al., 1995] to investigate surface wave transformation and breaking-induced nearshore circulation. The energy dissipation due to wave breaking is modeled by introducing an eddy viscosity term into the momentum equations, with the viscosity strongly localized on the front face of the breaking waves. Wave run-up on the beach is simulated using a moving shoreline technique. We employ quasi fourth-order finite difference schemes to solve the governing equations. Satisfactory agreement is found between the numerical results and the laboratory measurements of Haller et al. [1997], including wave height, mean water level, and longshore and cross-shore velocity components. The model results reveal the temporal and spatial variability of the wave-induced nearshore circulation, and the instability of the rip current in agreement with the physical experiment. Insights into the vorticity associated with the rip current and wave diffraction by underlying vortices are obtained.
195 citations
TL;DR: In this article, a finite-difference scheme for the electromagnetic field in 3D anisotropic media for electromagnetic logging was proposed, which has the following features: coercivity (i.e., the complete discrete analogy of all continuous equations in every grid cell, even for nondiagonal conductivity tensors), a special conductivity averaging, and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity.
Abstract: We consider a problem of computing the electromagnetic field in 3D anisotropic media for electromagnetic logging. The proposed finite-difference scheme for Maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis: coercivity (i.e., the complete discrete analogy of all continuous equations in every grid cell, even for nondiagonal conductivity tensors), a special conductivity averaging that does not require the grid to be small compared to layering or fractures, and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity. All of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3D geometries without sacrificing accuracy.
194 citations