This paper presents a comparative assessment of low Reynolds number k- models against standard k- model in an Eulerian framework. Three different low-Re number k- models: Launder-Sharma (LS), YangShih (YS) and AbeKondoh-Nagano (AKN) have been used for the description of bubble plume behaviour in stratified water. The contribution of the gas phase movement into the liquid phase turbulence has been achieved by using the Dispersed with Bubble Induced Turbulence approach (DIS+BIT). The results reveal that the oscillation frequency of gas-liquid flow are correctly reproduced by standard k- and LS models. In fact, we found for standard K- and LS a clear dominant peak at a frequency equal to 0. 1 Hz. On the other hand, YS and AKN models have predicted chaotic oscillations. The oscillation amplitude of the bubble plume predicted from LS model seems to be in good agreement with the PIV measurements of Besbes et al. (2015). However, for the standard K- model the oscillation amplitude is low. The air-water interface shows that the bubble plume mixing with the stratified water is predicted to be stronger compared to standard k- model.

Wave-field extrapolation based on solving the wave equation is an important step in seismic modeling and needs a high level of accuracy. It has been implemented through a various numerical methods such as finite difference method as the most popular and conventional one. Moreover, the main drawbacks of the finite difference method are the low level of accuracy and the numerical dispersion for large time intervals (Δ t). On the other hand, the symplectic integrators due to their structure can cope with this problem and act more accurately in comparison to the finite difference method. They reduce the computation cost and do not face numerical dispersion when time interval is increased. Therefore, the aim of the current paper is to present a symplectic integrator for wave-field extrapolation using the Euler method. Then, the extrapolation is implemented for rather large time intervals using a simple geological model. The extrapolation employed for both symplectic Euler and finite difference methods showed a better quality image for the proposed method. Finally the accuracy was compared to the finite difference method.

In this paper, a computational technique is presented based on the natural element method (NEM) for large plastic deformation simulation of the metal forming problems. NEM is a numerical technique in the field of computational mechanics and can be considered as a meshless method. The selected process is Backward extrusion for circular shape hollow components from round billets. The punch stroke value is divided into sub-steps, whereas a new set of nodes become active at the end of each sub-step of deformation. Solutions are obtained for different area reductions under friction condition. Hollman-Ludwik law is selected to explain the material behavior after the yielding point. The experiments are carried out with fully annealed commercial aluminum alloy billets at room temperature, using various punch sizes. A set of die and punches are designed and constructed for experimental works. The validity of the proposed method is verified by comparing the results from deformed geometry, contours of equivalent strain and forming loads with those obtained from finite element simulation and experimental measurements. It is concluded that the results obtained by NEM are in good agreement with those from FEM and experiments and therefore, the meshless natural element method is capable of handling large plastic deformation.

In this paper, we propose an exponential Euler method to approximate the solution of a stochastic functional differential equation driven by weighted fractional Brownian motion Ba, b under some assumptions on a and b. We obtain also the convergence rate of the method to the true solution after proving an L2-maximal bound for the stochastic integrals in this case.

The fractional-order differential equations (FDEs) have the ability to model the real-life phenomena better in a variety of applied mathematics, engineering disciplines including diffusive transport, electrical networks, electromagnetic theory, probability and so forth. In most cases, there are no analytical solutions therefore a variety of numerical methods have been developed for the solution of the FDEs. In this paper, we derive the numerical solutions of the various fractional-order Riccati type differential equations using the Euler Wavelet method (EWM). The Euler wavelet operational matrix method converts the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and efficiency of the technique.

In this work four algorithms are presented for the integration of equations governing the behavior of von Mises material in plastic limit. Two of them are single-step and the others are double-step algorithms. Single-step algorithms are straight forward extension of Backward Euler method or midpoint rule while double-step algorithms are a combination of two. In past similar algorithms were proposed for special cases of isotropic / kinematic hardening; however the algorithms presented in this work are applicable to general isotropic/kinematic hardening laws. Theoretical as well as numerical aspects are presented for all integration schemes and elaborated for double-step algorithms which are less explored in the literature. A comparison is made between the presented algorithms and the classical Backward Euler method.