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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, nine different methods of weighting interblock hydraulic conductivity values used for modeling one-dimensional water transfer in homogeneous unsaturated soil are tested for their influence upon the accuracy of the finite difference solution.
Abstract: Nine different methods of weighting interblock hydraulic conductivity values used for modeling one-dimensional water transfer in homogeneous unsaturated soil are tested for their influence upon the accuracy of the finite difference solution. On the basis of these results the most suitable weighting relation is selected. In a first stage the numerical results obtained by the models using the various conductivity weighting formulas are compared with the quasi-analytical solution developed by Philip for a clay soil. In a second stage the models are used to simulate a laboratory experiment carried out on a sandy soil. In both cases, rather drastic boundary conditions are applied. It appears clearly from these tests that the weighting errors are of critical influence on the accuracy of solution. As proposed in this note, the geometric mean taken over two adjacent hydraulic conductivity values is the only weighting method that generates little weighting error. The latter weighting relation is found to be preferable in terms of flexibility, precision, and feasibility.
142 citations
TL;DR: This work develops theory and numerical algorithms to apply level set methods to problems involving the transport and diffusion of material quantities in a level set framework and demonstrates the accuracy of this approach through a series of test examples and convergence studies.
142 citations
TL;DR: In this paper, the flow fields in two-dimensional channels with discontinuous expansions are studied numerically to understand how the channel expansion ratio influences the symmetric and nonsymmetric solutions that are known to occur.
Abstract: The flowfields in two-dimensional channels with discontinuous expansions are studied numerically to understand how the channel expansion ratio influences the symmetric and nonsymmetric solutions that are known to occur. For improved confidence and understanding, two distinct numerical techniques are used. The general flowfield characteristics in both symmetric and asymmetric regimes are ascertained by a time-marching finite difference procedure. The flowfields and the bifurcation structure of the steady solutions of the Navier-Stokes equations are determined independently using the finite element technique. The two procedures are then compared both as to their predicted critical Reynolds numbers and the resulting flowfield characteristics. Following this, both numerical procedures are compared with experiments.
142 citations
TL;DR: This paper generalizes a technique of anti-diffusive flux corrections, recently introduced by Despres and Lagoutiere for first-order schemes, to high order finite difference weighted essentially non-oscillatory (WENO) schemes to obtain sharp resolution for contact discontinuities.
141 citations
TL;DR: In this paper, the authors developed a fourth-order compact scheme for the approximation of first and second derivatives on non-uniform meshes, which includes metrics in the coefficients of the compact scheme instead of methods using Jacobian transformation.
Abstract: In this paper, the development of a fourth- (respectively third-) order compact scheme for the approximation of first (respectively second) derivatives on non-uniform meshes is studied. A full inclusion of metrics in the coefficients of the compact scheme is proposed, instead of methods using Jacobian transformation. In the second part, an analysis of the numerical scheme is presented. A numerical analysis of truncation errors, a Fourier analysis completed by stability calculations in terms of both semi- and fully discrete eigenvalue problems are presented. In those eigenvalue problems, the pure convection equation for the first derivative, and the pure diffusion equation for the second derivative are considered. The last part of this paper is dedicated to an application of the numerical method to the simulation of a compressible flow requiring variable mesh size: the direct numerical simulation of compressible turbulent channel flow. Present results are compared with both experimental and other numerical (DNS) data in the literature. The effects of compressibility and acoustic waves on the turbulent flow structure are discussed.
140 citations