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: The quasi-stationary state approximation to mass transport and fluid-rock interaction provides a quantitative description of metasomatic processes over geologically significant time spans as discussed by the authors, which is valid if mineral reaction zone boundaries, surface area, porosity and permeability change slowly compared to the time required to establish a stationary state.
359 citations
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01 Jan 2000TL;DR: This paper presents a simple and effective technique for handling negative linear weights without a need to get rid of them and test cases are shown to illustrate the stability and accuracy of this approach.
Abstract: High-order accurate weighted essentially nonoscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structured and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a higher order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative, such as in the central WENO schemes using staggered meshes, high-order finite volume WENO schemes in two space dimensions, and finite difference WENO approximations for second derivatives. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. The previous strategy for handling this difficulty is either by regrouping of stencils or by reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them. Test cases are shown to illustrate the stability and accuracy of this approach.
356 citations
354 citations
TL;DR: The numerical results show that the proposed continuous genetic algorithm is a robust and accurate procedure for solving systems of second-order boundary value problems and the obtained accuracy for the solutions using CGA is much better than the results obtained using some modern methods.
352 citations
TL;DR: In this paper, a general procedure for deriving equations for numerical work from the equations of hydrodynamics is described, applied to the derivation of the SPH equations which conserve linear and angular momentum exactly.
Abstract: The theme of this paper is that particle methods are closely related to both finite difference and spectral methods because the three methods can be considered special cases of interpolation by kernel estimation. The kernels for a number of special cases are given in detail, and the accuracy of the resulting interpolation is analyzed. A general procedure for deriving equations for numerical work from the equations of hydrodynamics is described. It is applied to the derivation of the SPH equations which conserve linear and angular momentum exactly.
351 citations