scholarly journals A general linear method approach to the design and optimization of efficient, accurate, and easily implemented time-stepping methods in CFD

2022 ◽  
pp. 110927
Author(s):  
Victor DeCaria ◽  
Sigal Gottlieb ◽  
Zachary J. Grant ◽  
William J. Layton
Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 381 ◽  
Author(s):  
Zanariah Abdul Majid ◽  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Fudziah Ismail

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson’s rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods.


2019 ◽  
Vol 9 (4) ◽  
pp. 433-444 ◽  
Author(s):  
Faranak Rabiei ◽  
◽  
Fatin Abd Hamid ◽  
Zanariah Abd Majid ◽  
Fudziah Ismail ◽  
...  

2017 ◽  
Vol 9 (9) ◽  
pp. 168781401771541 ◽  
Author(s):  
Faranak Rabiei ◽  
Fatin Abd Hamid ◽  
Mohammad M Rashidi ◽  
Fudziah Ismail

2021 ◽  
Vol 10 (1) ◽  
pp. 94-126
Author(s):  
Basem Attili

This article considers the numerical simulation of fuzzy two-point boundary value problems (FBVP) using general linear method (GLM). The author derived the method, which is a combination of a Runge-Kutta type method and multi-step method. It is originally designed to solve initial value problems. It requires fewer function evaluations than the traditional Runge-Kutta methods making it computationally more efficient in achieving the required accuracy. The author will utilize the combination of the GLM with initial value methods to solve the linear fuzzy BVP's and a shooting-like method for the nonlinear cases. Numerical testing and simulation of several examples, considered by other authors, will be presented to show the efficiency of the proposed method.


Author(s):  
Günther F. Clauss ◽  
Marco Klein ◽  
Carlos Guedes Soares ◽  
Nuno Fonseca

In the last years the identification and investigation of critical wave sequences regarding offshore structure responses became one of the main topics in the ocean engineering community. Thereby the area of interest covers the entire field of application spectra at sea — from efficient and economic offshore operations in moderate sea states to reliability as well as survival in extreme wave conditions. For most cases, the focus lies on limiting criteria for the design, such as maximum global loads, maximum relative motions between two or more vessels or maximum accelerations, at which the floating structure has to operate or to survive. These criteria are typically combined with a limiting characteristic sea state (Hs, Tp) or a rogue wave. For the investigation of offshore structures as well as the identification of critical wave sequences, different approaches are available — most of them are based on linear transfer functions as it is an efficient procedure for the fast holistic evaluation. But, for some cases the linear method approach implies uncertainties due to nonlinear response behavior, in particular in extreme wave conditions. This paper presents an approach to these challenges, a response based optimization tool for critical wave sequence detection. This tool, which has been successfully introduced for the evaluation of the applicability of a multi-body system based on the linear method approach, is adjusted to a nonlinear task — the vertical bending moment of a chemical tanker in extreme wave conditions. Therefore a nonlinear strip theory solver is introduced into the optimization routine to capture the nonlinear effects on the vertical bending moment due to steep waves acting on large bow flares. The goal of the procedure is to find a worst case wave sequence for a certain critical sea state. This includes intensive numerical investigation as well as model test validation.


Sign in / Sign up

Export Citation Format

Share Document