Abstract

The field of fluid-structure interaction (FSI) has important
applications ranging from the bio-medical to the civil and
aeronautical engineering fields. Despite the different approaches
developed over recent years the general solution of FSI problems
remains however far from being closed. This paper addresses the
theoretical analysis of a several partitioned solution schemes
 for FSI. This is achieved by choosing a simple but
representative model problem which allows to obtain analytical
results. A loose coupling partitioned procedure is presented
first. An iterative version of the same algorithm is presented
next together with an analysis of its convergence properties and a
brief discussion of a possible acceleration strategy. Finally a
new iterative strategy based on solving a modified equation
 is described. Some examples of application of the
partitioned algorithms considered are presented including the
aeroelastic analysis of a bridge.

Abstract

Abstract

Abstract

Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton–Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Padé polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers.

Abstract

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ=ζ(Re, ε∗, λ)which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as threeor two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džuni´c–Petkovi´c–Petkovi´c; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.