Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.

On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws

This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.

A new slope optimization design based on limit curve method

A new method is proposed for slope optimization design based on the limit curve method, where the slope is in the limit equilibrium state when the limit slope curve determined by the slip-line field theory and the slope intersect at the toe of the slope. Compared with the strength reduction (SR) method, finite element limit analysis method, and the SR method based on Davis algorithm, the new method is suitable for determining the slope stability and limit slope angle (LSA). The optimal slope shape is determined based on a series of slope heights and LSA values, which increases the LSA by 2.45°-11.14° and reduces an invalid overburden amount of rocks by 9.15%, compared with the space mechanics theory. The proposed method gives the objective quantification index of instability criterion, and results in a significant engineering economy.

Slope stability analysis of Southern slope of Chengmenshan copper mine,China

The engineering geology and hydrogeology in the southern slope of Chengmenshan copper mine are very complicated,because there is a soft-weak layer between two kinds of sandstones.Field investigations demonstrate that some instability problems might occur in the slope.In this research,the southern slope,which is divided into six sections(I-0,I-1,I-2,II-0,II-1 and II-2),is selected for slope stability analysis using limit equilibrium and numerical method.Stability results show that the values of factor of safety(FOS) of sections I-0,I-1 and I-2 are very low and slope failure is likely to happen.Therefore reinforcement subjected to seismic,water and weak layer according to sections were carried out to increase the factor of safety of the three sections,two methods were used;grouting with hydration of cement and water to increase the cohesion(c) and pre-stressed anchor.Results of reinforcement showed that factor of safety increased more than 1.15.

Stability analysis for natural slope by kinematical approach

The stability of natural slope was analyzed on the basis of limit analysis. The sliding model of a kind of natural slope was presented. A new kinematically admissible velocity field for the new sliding model was constructed. The stability factor formulation by the upper bound theorem leads to a classical nonlinear programming problem, when the external work rate and internal energy dissipation were solved, and the constraint condition of the programming problem was given. The upper bound optimization problem can be solved efficiently by applying a nonlinear SQP algorithm, and stability factor was obtained, which agrees well with previous achievements.

Soil Atterberg Limits and Consistency Indices as Influenced by Land Use and Slope Position in Western Iran

Atterberg limits and consistency indices are used for classifications of cohesive(fine-grained) soils in relation with compaction and tillage practices. They also provide information for interpreting several soil mechanical and physical properties such as shear strength, compressibility, shrinkage and swelling potentials. Although, several studies have been conducted regarding the land use effects on various soil mechanical properties, little is known about the effects of land use and slope positions on Atterberg limits and consistency indices. This study was conducted to investigate the effects of land use and slope position on selected soil physical and chemical properties, Atterberg limits and consistency indices in hilly region of western Iran. Three land uses including dryland farming, irrigated farming and pasture and four slope positions(i.e., shoulder, backslope, footslope, and toeslope) were used for soil samplings. One hundred eleven soil samples were collected from the surface soil(0-10 cm). Selected physical and chemical properties, liquid limit(LL), plastic limit(PL) and shrinkage limit(SL) were measured using the standard methods; and consistency indices including plastic index(PI), friability index(FI), shrinkage index(SI) and soil activity(A=PI/clay) were calculated. The results showed that irrigated farming significantly increased organic matter content(OM) and OM/clay ratio, and decreased bulk density(ρb) and relative bulk density(ρb-rel) as a result of higher biomass production and plant residues added to the soil compared to other land uses. Except for sand content, OM, ρb, cation exchange capacity(CEC) and calcium carbonate equivalent(CCE), slope position significantly affected soil physical and chemical properties. The highest values of silt, OM/clay and CEC/clay were found in the toeslope position, predominantly induced by soil redistribution within the landscape. The use of complexed(COC)- noncomplexed organic carbon(NCOC) concept indicated that majority of the studied soils were located below the saturation line and the OM in the soils was mainly in the COC form. The LL, PI, FI and A showed significant differences among the land uses; the highest values belonged to the irrigated farming due to high biomass production and plant residues returned to the soils. Furthermore, slope position significantly affected the Atterberg limits and consistency indices except for SL. The highest values of LL, PI, SI and A were observed in the toeslope position probably because of higher OM and CEC/clay due to greater amount of expandable phyllosilicate clays. Overall, soils on the toeslope under irrigated farming with high LL and SI and low values of FI need careful tillage management to avoid soil compaction.

New algorithm of mine slope reliability based on limiting state hyper-plane and its engineering application

Due to the influence of joint fissure, mining intensity, designed slope angle, underground water and rainfall, the failure process of mine slope project is extremely complicated. The current safety factor calculation method has certain limitations, and it would be difficult to obtain the reliability index when the performance function of reliability analysis is implicit or has high order terms. Therefore, with the help of the logistic equation of chaos theory, a new algorithm of mine slope reliability based on limiting state hyper-plane is proposed. It is shown that by using this new reliability algorithm the calculation of partial derivative of performance function is avoided, and it has the advantages of being simple and easy to program. The new algorithm is suitable for calculating the reliability index of complex performance function containing high order terms. Furthermore, the limiting state hyper-plane models of both simplified Bishop's and Janbu's method adaptive to slope project are obtained, and have achieved satisfactory effect in the study of mine slope stability in Dexing copper open pit.

Liquid-plastic Limit of Surface Sediments in North Slope of South China Sea

1 Introduction China has a vast area of continental shelf and is very rich in marine resources,but because of the complex geological environment and frequent geological disasters,the utilization of marine resources and the construction of marine engineering are limited(Zhu et al.,2016).As the

Effect of channel shape on selection of time marching scheme in the discontinuous Galerkin method for 1-D open channel flow

One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth （multistep）, and second-order total variation diminishing （TVD） Runge-Kutta （multistage） time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic （rectangular, trapezoidal, triangular, and parabolic cross-sections） and non-prismatic （natural river） channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.

A fully-explicit discontinuous Galerkin hydrodynamic model for variably-saturated porous media

Groundwater flows play a key role in the recharge of aquifers, the transport of solutes through subsurface systems or the control of surface runoff. Predicting these processes requires the use of groundwater models with their applicability directly linked to their accuracy and computational efficiency. In this paper, we present a new method to model water dynamics in variably- saturated porous media. Our model is based on a fully-explicit discontinuous-Galerkin formulation of the 3D Richards equation, which shows a perfect scaling on parallel architectures. We make use of an adapted jump penalty term for the discontinuous-Galerkin scheme and of a slope limiter algorithm to produce oscillation-free exactly conservative solutions. We show that such an approach is particularly well suited to infiltration fronts. The model results are in good agreement with the reference model Hydrus-lD and seem promising for large scale applications involving a coarse representation of saturated soil.

GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations

We discuss the development,verification,and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations.The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations.Our algorithms are tailored to take advantage of the single instruction multiple data(SIMD)architecture of graphic processing units.The time integration is accelerated by local time stepping based on a multi-rate Adams-Bashforth scheme.A total variational bounded limiter is adopted for nonlinear stability of the numerical scheme.This limiter is coupled with a mass and momentum conserving positivity preserving limiter for the special treatment of a dry or partially wet element in the triangulation.Accuracy,robustness and performance are demonstrated with the aid of test cases.Furthermore,we developed a unified multi-threading model OCCA.The kernels expressed in OCCA model can be cross-compiled with multi-threading models OpenCL,CUDA,and OpenMP.We compare the performance of the OCCA kernels when cross-compiled with these models.