Disaster Chain Analysis of Landfill Landslide: Scenario Simulation and Chain-Cutting Modeling

Landfill landslide is a man-made event that occurs when poorly managed garbage mounds at landfills collapse. It has become common in recent decades due to the rising waste volumes in cities. Normally, it is a complex process involving many disaster-causing factors and composed by many sequential sub-events. However, most current studies treat the landslide as a single and independent event and cannot give a full picture of the disaster. We propose a disaster chain analysis framework for landfill landslide in terms of scenario simulation and chain-cutting modeling. Each stage of the landfill landslide is modeled by taking advantage of various advanced techniques, e.g., remote sensing, 3DGIS, non-Newtonian fluid model, central finite difference scheme, and agent-base steering model. The 2015 Shenzhen “1220” landslide was firstly reviewed to summarize the general disaster chain model for landfill landslide. Guided by this model, we then proposed the specific steps for landfill landslide disaster chain analysis and applied them to another undergoing landfill, i.e., Xinwuwei landfill in Shenzhen, China. The scenario simulation in this landfill provides suggestions on potential hazardous risks and some applicable treatments. Through chain-cutting modeling, we further validated the effectiveness and feasibility of these treatments. The most optimized solution is subsequently deduced, which can provide support for disaster prevention and mitigation for this landfill.

High-order conservative formulation of viscous terms for variable viscosity flows

The work presents a general strategy to design high-order conservative co-located finite-difference approximations of viscous/diffusion terms for flows featuring extreme variations of diffusive properties. The proposed scheme becomes equivalent to central finite-difference derivatives with corresponding order in the case of uniform flow properties, while in variable viscosity/diffusion conditions it grants a strong preservation and a proper telescoping of viscous/diffusion terms. Presented tests show that standard co-located discretisation of the viscous terms is not able to describe the flow when the viscosity field experiences substantial variations, while the proposed method always reproduces the correct behaviour. Thus, the process is recommended for such flows whose viscosity field highly varies, in both laminar and turbulent conditions, relying on a more robust approximation of diffuse terms in any situation. Hence, the proposed discretisation should be used in all these cases and, for example, in large eddy simulations of turbulent wall flows where the eddy viscosity abruptly changes in the near-wall region.

Underground polymeric l-shaped pipeline vibrations under seismic effect

The simultaneous equations of longitudinal and transverse vibrations of an underground polymeric L-shaped pipeline under the arbitrary direction of seismic load were derived in the paper. A computational scheme of the problem was constructed using central finite-difference relations. The analysis of the results obtained on the simultaneous longitudinal and transverse vibrations of underground polymeric L-shaped pipelines under seismic loading was conducted. The stress-strain state of the L-shaped polymeric pipeline subjected to seismic effect was determined, and the axial forces and bending moments arising in curved pipelines during an earthquake were determined.

Error estimation of the Besse relaxation scheme for a semilinear heat equation

The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse Relaxation Scheme in time [C. R. Acad. Sci. Paris S{\'e}r. I, vol. 326 (1998)] with a central finite difference method in space. A new, composite stability argument is developed, leading to an optimal, second-order error estimate in the discrete $L_t^{\infty}(H_x^2)-$norm at the time-nodes and in the discrete $L_t^{\infty}(H_x^1)-$norm at the intermediate time-nodes. It is the first time in the literature where the Besse Relaxation Scheme is applied and analysed in the context of parabolic equations.

AN OVERLAPPING SCHWARZ METHOD FOR SINGULARLY PERTURBED FOURTH-ORDER CONVECTION-DIFFUSION TYPE

In this paper, we have constructed an iterative numerical method based on an overlapping Schwarz procedure with uniform mesh for singularly perturbed fourth-order of convection-diffusion type. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the method produces numerical approximations which converge in the maximum norm to the exact solution. We prove that, when appropriate subdomains are used the method produces convergence of almost second-order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results.

A Comparison Study of HO-CFD and DSC-RSK with Small Computational Bandwidths for Solving Some Classes of Boundary-Value and Eigenvalue Problems

This paper conducts a comparison analysis of high order central finite difference (HO-CFD) method and discrete singular convolution-regularized Shannon kernel (DSC-RSK) scheme with small computational bandwidths for solving some classes of boundary-value and eigenvalue problems. Second-, fourth- and sixth-order partial differential equations are taken into account. New strategies to generate parameters [Formula: see text] in DSC-RSK are proposed to ensure minimum errors for each case, and the influence of parameters [Formula: see text] with more decimal places is analyzed. Apart from the existing matched interface and boundary (MIB) scheme, a new double-parameter MIB scheme is also proposed. The influence of small computational bandwidths is discussed in detail. Numerical results by using HO-CFD and DSC-RSK are presented and compared to illustrate the performance of both methods in small bandwidth limit. Some remarkable conclusions have been drawn at the end of this study.

A NUMERICAL SCHEME FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE ON AN ADAPTIVE GRID

In this paper, an adaptive mesh strategy is presented for solving singularly perturbed delay differential equation of convection-diffusion type using second order central finite difference scheme. Layer adaptive meshes are generated via an entropy production operator. The details of the location and width of the layer is not required in the proposed method unlike the popular layer adaptive meshes mainly by Bakhvalov and Shishkin. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

SEMI-ANALYTICAL SOLUTION OF THE HEAT CONDUCTION IN A PLATE WITH HEAT GENERATION

In the present work, a formulation for the solution of the two-dimensional steady state heat conduction with heat generation is presented. The classical integral transform technique (CITT) is used to solve the problem in a semi- analytical manner. CITT deals with expansions of the sought solution in terms of infinite orthogonal basis of eigenfunctions, keeping the solution process always within a continuous domain. For the particular problem, the resulting system is composed of a set of uncoupled differential equations which can be solved analytically. However, a truncation error is involved since the infinite series must be truncated to obtain numerical results. For comparison and validation purposes, the second order central finite difference method (FDM) is also implemented. The convergence analysis showed that CITT has a greater performance having no difficulties to obtain accurate results with very few terms in the solution summation. The FDM had convergence troubles specially for the positions near the center and for high concentration of heat generation in the center of the plate.

Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation

This paper has employed a comparative study between the numerical scheme and stability condition. Numerical calculations are carried out based on three different numerical schemes, namely the central finite difference, fourier leap-frog, and fourier spectral RK4 schemes. Stability criteria for different numerical schemes are developed for the KdV equation, and numerical examples are put to test to illustrate the accuracy and stability between the solution profile and numerical scheme.