Momentum Conservative Schemes for Shallow Water Flows

We discuss the implementation of the finite volume method on a staggeredgrid to solve the full shallow water equations with a conservative approximation forthe advection term. Stelling & Duinmeijer [15] noted that the advection approximationmay be energy-head or momentum conservative, and if suitable which of these toimplement depends upon the particular flow being considered. The momentum conservativescheme pursued here is shown to be suitable for 1D problems such as transcriticalflow with a shock and dam break over a rectangular bed, and we also found that oursimulation of dam break over a dry sloping bed is in good agreement with the exactsolution. Further, the results obtained using the generalized momentum conservativeapproximation for 2D shallow water equations to simulate wave run up on a conicalisland are in good agreement with benchmark experimental data.

Undrained capacity of a hybrid subsea skirted mat with caissons under combined loading

Skirted mudmats are commonly used to support offshore infrastructure. However, these may not be able to provide sufficient capacity to notably withstand the lateral loads applied by jumpers and connectors. The concept of hybrid foundation system was therefore proposed to enhance the capacity in a targeted fashion, through addition of internal suction caisson compartments. This paper presents a numerical investigation into the undrained bearing capacity of a rectangular-shaped hybrid foundation with two caisson units. Uniaxial capacities under vertical, horizontal, and moment loading are reported, but the focus lies on the horizontal–moment planes due to the anticipated low vertical load on the foundation. Detailed discussion highlights the contribution of the internal caisson compartments to the significant increases in horizontal capacity compared to a simple rectangular skirted mat through changes in the failure mechanism. This results not only in changes in size, but also in shape, of the capacity envelope. The study was extended to more general horizontal–moment loading conditions, where the shape of the capacity envelope was found to remain approximately constant. This applies to the hybrid foundation and the rectangular skirted mat in the homogeneous soil considered here. An expression is proposed that provides a slightly conservative approximation of the capacity envelope under combined horizontal and moment loading from any direction.

Momentum Conservative Schemes for Shallow Water Flows

We discuss the implementation of the finite volume method on a staggered grid to solve the full shallow water equations with a conservative approximation for the advection term. Stelling & Duinmeijer [15] noted that the advection approximation may be energy-head or momentum conservative, and if suitable which of these to implement depends upon the particular flow being considered. The momentum conservative scheme pursued here is shown to be suitable for 1D problems such as transcritical flow with a shock and dam break over a rectangular bed, and we also found that our simulation of dam break over a dry sloping bed is in good agreement with the exact solution. Further, the results obtained using the generalised momentum conservative approximation for 2D shallow water equations to simulate wave run up on a conical island are in good agreement with benchmark experimental data.

A Practical Computing Method for Residual Area of Rebar Cross-Sections under Carbonation Induced Corrosion

Area loss of severely weakened rebar cross sections is a crucial variable in assessment of structural deterioration for corroded concrete structures, which is hard to be measured or estimated precisely in conventional methods. In this paper, rebar samples were taken from naturally corroded RC slabs. Their virtual models were built using 3D laser scanning technique to facilitate geometric measurement. From these models seriously weakened sections were screened out as analyzing samples, and residual areas as well as profiles of the cross-sections were derived and investigated consequently. Shown by the results, corrosion was non-uniformly distributed on rebar surface, and profiles of the residual cross-sections can hardly be formulated efficiently. However, they can be simplified into ellipse with minor axis of minimum residual diameter and major axis of diameter in perpendicular direction. This model has been proved to give an conservative approximation of residual sectional area with 4.27% underestimation and 89.2% degree of confidence.

A Numerical Method for Two-Stage Stochastic Programs under Uncertainty

Motivated by problems coming from planning and operational management in power generation companies, this work extends the traditional two-stage linear stochastic program by adding probabilistic constraints in the second stage. In this work we describe, under special assumptions, how the two-stage stochastic programs with mixed probabilities can be treated computationally. We obtain a convex conservative approximations of the chance constraints defined in second stage of our model and use Monte Carlo simulation techniques for approximating the expectation function in the first stage by the average. This approach raises with another question: how to solve the linear program with the convex conservative approximation (nonlinear constrains) for each scenario?

Law and aesthetics: critical note

It is thought in the theory and philosophy of law, aimed at discussing the conditions of possibility of rapprochement between the art form and legal form. The text investigates, dialectically, the implications for the legal philosophy of the impossibility of such approximation, and the problems in a conservative approximation. It follows that: 1) would be a loss for a reason and therefore to legal philosophy, not to communicate between art and law; 2) the relationship between legal and aesthetic standards should be guided by the critical, especially in terms of Adorno's thought. It is by overcoming the dichotomy between possibility and impossibility, opening on the idea of constellation of methodological categorical fields of law and aesthetics in their current forms, paving the way for understanding the legal form as a tragic way.