Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for $3\times 3$ hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to $2\times 2$ system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.

Reservoir sedimentation can result in loss of much needed reservoir storage capacity, reducing the useful life of dams. Thus, sufficient sediment storage capacity should be provided for the reservoir design stage to ensure that sediment accumulation will not impair the functioning of the reservoir during the useful operational-economic life of the project. However, an important issue to consider when estimating reservoir sedimentation and accumulation is the uncertainty involved in reservoir sedimentation. In this paper, the basic factors influencing the density of sediments deposited in reservoirs are discussed, and uncertainties in reservoir sedimentation have been determined using the Delta method. Further, Kenny Reservoir in the White River Basin in northwestern Colorado was selected to determine the density of deposits in the reservoir and the coefficient of variation. The results of this investigation have indicated that by using the Delta method in the case of Kenny Reservoir, the uncertainty regarding accumulated sediment density, expressed by the coefficient of variation for a period of 50 years of reservoir operation, could be reduced to about 10%. Results of the Delta method suggest an applicable approach for dead storage planning via interfacing with uncertainties associated with reservoir sedimentation.

A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem.

Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.

Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. A laterally heated square enclosure, filled with air, was studied. A FORTRAN code based on the lattice Boltzmann method (LBM) was developed for this purpose. The finite difference method was applied to discretize the LBM equations. Furthermore, for comparison purpose, the commercially available CFD package FLUENT, which uses finite volume Method (FVM), was also used to simulate the same problem. Different discretization schemes, being the first order upwind, second order upwind, power law, and QUICK, were used with the finite volume solver where the SIMPLE and SIMPLEC algorithms linked the velocity-pressure terms. The results were also compared with existing experimental and numerical data. It was observed that the finite volume method requires less CPU usage time and yields more accurate results compared to the LBM. It has been noted that the 1st order upwind/SIMPLEC combination converges comparatively quickly with a very high accuracy especially at the boundaries. Interestingly, all variants of FVM discretization/pressure-velocity linking methods lead to almost the same number of iterations to converge but higher-order schemes ask for longer iterations.

This paper focuses on the problem of hedging against seismic risk through the retrofit of transportation systems in large-scale construction projects (LSCP). A fuzzy random multiobjective bilevel programming model is formulated with the objectives of the retrofit costs and the benefits on two separate levels. After establishing the model, a fuzzy random variable transformation approach and fuzzy variable approximation decomposition are used to deal with the uncertainty. An approximation decomposition-based multi-objective AGLNPSO is developed to solve the model. The results of a case study validate the efficiency of the proposed approach.

The well-known Blasius flow is governed by a third-order nonlinear ordinary differential equation with two-point boundary value. Specially, one of the boundary conditions is asymptotically assigned on the first derivative at infinity, which is the main challenge on handling this problem. Through introducing two transformations not only for independent variable bur also for function, the difficulty originated from the semi-infinite interval and asymptotic boundary condition is overcome. The deduced nonlinear differential equation is subsequently investigated with the fixed point method, so the original complex nonlinear equation is replaced by a series of integrable linear equations. Meanwhile, in order to improve the convergence and stability of iteration procedure, a sequence of relaxation factors is introduced in the framework of fixed point method and determined by the steepest descent seeking algorithm in a convenient manner.