Finite Dierence Method Research Articles

Finite Dierence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition

Finite Dierence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition

Uncertainty assessment of critical excavation depth of vertical unsupported cuts in undrained clay using random eld theorem

Classical methods such as limit equilibrium or limit analysis, dealing with the stability analysis of open cuts and trenches and calculation of critical excavation depth for them, do not fully satisfy the theoretical requirements for stability problems leading to di erent solutions depending on the adopted method. It is now appreciated that geomaterials exhibit considerable heterogeneity, caused by the lithological and inherent variation, which cannot be fully covered by simple methods. This paper highlights the uncertainty embedded in critical excavation depth calculation, arising from spatial variability of shear strength parameters, using Random Finite Di erence Method (RFDM) and Random Limit Equilibrium Method (RLEM). In the present study, the lognormally distributed undrained shear strength is considered spatially correlated throughout the domain. Surface cohesion value and the shear strength density were introduced as the deterministic parameters along with the coecient of variation of undrained shear strength and its scale of uctuation as stochastic parameters; these parameters were studied to see their e ect on uncertainty in critical excavation depth estimation. The results clearly demonstrated the uncertainty in critical excavation depth arising from the inherent variability of shear strength parameters using the RFDM results; however, RLEM did not prove to reflect such uncertainty eciently due to local averaging in prescribed failure surfaces.

A SEMI-LAGRANGIAN METHOD BASED ON WENO INTERPOLATION

Abstract. In this paper, a general Weighted Essentially Non-Oscillatory (WENO) interpolation is proposed and applied to asemi-Lagrangian method. The proposed method is based on theconservation law, and characteristic curves are used to completethe semi-Lagrangian method. Therefore, the proposed method sat-is es conservation of mass and is free of the CFL condition whichis a necessary condition for convergence.Using a several standardexamples, the proposed method is compared with the third orderStrong Stability Preserving (SSP) Runge-Kutta method to verifythe high-order accuracy. 1. IntroductionThe Weighted Essentially Non-Oscillatory (WENO) interpolations[8, 9, 10, 12, 13] are well known e ective high-order non-oscillatoryschemes based on Eulerian approach methods (grid based methods) asFinite Volume methods (FVM) or Finite Di erence methods (FDM).However, one of the drawbacks is that the methods are limited by theCourant-Friedrichs-Levy (CFL) condition which is a necessary conditionfor convergence.In order to resolve this challenging problem, a semi-Lagrangian methodconstructed by characteristic curves and grid points is introduced [1, 2, 3,4, 5, 14]. Our main idea is that time integration of a given conservationlaw (a partial di erential eqnarray to be solved) is changed into space in-tegration by using characteristic curves as the semi-Lagrangian method,and the Gaussian quadrature rule to obtain high-order accuracy. There-fore, it can not be guaranteed that the points of Gaussian quadraturerule computed by the characteristic curves are on regula grid points

Stochastic perturbation approach to the wavelet‐based analysis

AbstractThe wavelet‐based decomposition of random variables and fields is proposed here in the context of application of the stochastic second order perturbation technique. A general methodology is employed for the first two probabilistic moments of a linear algebraic equations system solution, which are obtained instead of a single solution projection in the deterministic case. The perturbation approach application allows determination of the closed formulas for a wavelet decomposition of random fields. Next, these formulas are tested by symbolic projection of some elementary random field. Copyright © 2004 John Wiley & Sons, Ltd.