First order perturbation approach for the free surface flow over a step with large Weber number

The problem of two-dimensional free surface flow of inviscid and incompressible fluid over a step is considered. The flow is assumed to be as steady and irrotational, the effect of the surface tension is considered, but the gravity force is neglected. This problem is characterized by the nonlinear condition given by Bernoulli's equation on the unknown free surface, which can be considered as part of the solution. The main purpose of this work is to give an approximate solution of this problem, by using the Hilbert transformation and the perturbation technique; the results are calculated for a large values of the Weber number and small inclination angle of the step values. These results demonstrate that the used method is easily implemented, and provides approximate solutions to these kinds of problems.

PC-solutions and quasi-solutions of the interval system of linear algebraic equations

The problem of solving the interval system of linear algebraic equations (ISLAEs) is one of the well-known problems of interval analysis, which is currently undergoing intensive development. In general, this solution represents a set, which may be given differently, de- pending on which quantifiers are related to the elements of the left and right sides of this system. Each set of solutions of ISLAE to be determined is described by the domain of compatibility of the corresponding system of linear inequalities and, normally, one nonlinear condition of the type of complementarity. It is difficult to work with them when solving specific problems. Therefore, in the case of nonemptiness in the process of solving the problem it is recommended to find a so-called PC-solution, based on the application of the technique known in the theory of multi-criterial choice, that presumes maximization of the solving capacity of the system of inequalities. If this set is empty, it is recommended to find a quasi- solution of ISLAE. The authors compare the approach proposed for finding PC- and/or quasi-solutions to the approach proposed by S. P. Shary, which is based on the application of the recognizing functional.

Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition

In the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time fractional diffusion equation from an additional measurement in the form of an integral over the space domain. First we study the existence, uniqueness, regularity and stability of the solution for the direct problem by using the fixed point theorem. And we obtain the uniqueness of the inverse time-dependent potential term problem. Numerically, we use the Levenberg–Marquardt method to find the approximate potential function. Four different examples are presented to show the feasibility and efficiency of the proposed method.

FEM Considerations to Simulate Interlocked Bladed Disks With Lagrange Multipliers

A few structural simulation issues with constrained Finite Elements using Lagrange multipliers are described. The main difficulties associated to interlocked bladed disks are: 1. Contacts. The structural state must be calculated by the FEM solver accounting the centrifugal, thermal and pressure loads. The interlock surfaces may slide, some area will be in contact and some others will be separated. This is a nonlinear condition that needs solver iterations. 2. Interference. The blade surfaces susceptible to contact are not necessarily periodic. In many cases pretwist is needed during assembly to couple the blades. The solution for surfaces in contact require a cyclic symmetry boundary condition. Different issues related to coordinates systems will be discussed. 3. Overconstraint. The model mesh nodes may accommodate more than one boundary condition. Interlock nodes are affected for both conditions, possibility of contact and cyclic symmetry. The use of Lagrange multipliers may cope with these problems. This is a well-known method although some FEM methodology peculiarities will be derived from scratch, either in the static and modal simulations. Pros and cons of this approach will be discussed related to classical solutions to the aforementioned problems. Every algorithm described has been already implemented in a FEM code than runs with successful results.

Disturbance Observer Assisted Error Sensitive Predictive Control for Induction Motors in Sensor less Environment: A Vector Field Control Model

The exponentially rise within the demands of Induction Motors in several applications has revitalized academia-industries to develop more robust and efficient IM drives. Amongst the main classically available IM drives efforts are made either to regulate speed or torque. However, the problem inculcated due to parametric mismatch and resulting errors have much addressed. Though, predictive control based approaches are found potential to help current and torque control; however, ensuring optimal controllability under nonlinear condition remained a tedious task. Filter based approaches to impose delay that eventually impacts overall control performance. Realizing it as motivation, during this research a highly robust Disturbance Observer Assisted Error Sensitive Predictive Control Strategy for IM control is developed. Subsequently, a completely unique Disturbance Observer-based Model Predictive Control strategy is developed that performs predictive current control and torque-control during a non-linear environment. Our proposed model exploits the concept of Prediction-Error to realize transient controllability. Exploiting the error information our proposed model identified the optimal voltage vector value to be injected to the 3-∅ inverter connected to the PI-based Space Vector Pulse Width Modulation system to perform transient controllability. Structurally, our proposed system encompasses SQIM motor, 3-∅ inverter, PI controller SVPWM, Fluxobserver, Torque and Speed controllers, VSI units, etc. The MATLAB 2017a based simulation has revealed that the proposed model is able to do better current control, flux-torque control and torque-ripple suppression, which broadened its employability for varied applications demands fast-torque control during a noisy environment