Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this paper, a time-splitting spectral approximation for the Schrodinger equation in the semiclassical regime is proposed. But the authors consider the case where the Planck constant e is small and require the spatial mesh size h = O(e) and the time step k = o(e).
401 citations
TL;DR: Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet's boundary conditions with the unique advantage of the Barakat and Clark technique, which is unconditionally stable and is explicit in nature.
400 citations
TL;DR: The comparison with the corresponding results of finite difference methods by the L1 formula demonstrates that the new L1-2 formula is much more effective and more accurate than the L2 formula when solving time-fractional differential equations numerically.
400 citations
Book•
01 May 1982
TL;DR: An overview of the fundamental concepts and applications of computerized groundwater modeling can be found in this paper, where the authors present an overview of some of the basic concepts and application of groundwater modeling.
Abstract: Introduction to Groundwater Modeling presents an overview of the fundamental concepts and applications of computerized groundwater modeling.
399 citations
TL;DR: In this paper, the authors simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization.
Abstract: We have simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization. Detailed comparisons of turbulence statistics and energy spectra in the downstream wake region (7.0 < x/D < 10.0) have been made with the results of Beaudan and Moin and with experiments to assess the impact of numerical diffusion on the flowfield. Based on these comparisons, conclusions are drawn on the suitability of higher-order upwind schemes for LES in complex geometries.
397 citations