least-squares method

This article aims to investigate the stability and estimate the aerodynamic coefficients of an aircraft based on experimental flight data. The least squares method was used to estimate these coefficients by using data from an inertial measurement unit (IMU) and global positioning system (GPS). This research, for the first time, has estimated these coefficients on a high-wing aircraft and during various flight maneuvers, including takeoff, landing and variant turns. It has been conducted utilizing time and frequency response data based on actual flight. In this article, the match between the recorded flight path of the aircraft and the flight path plotted by MATLAB software output was evaluated, and the output of the flight path model confirmed this match. Moreover, to improve the estimation of aerodynamic coefficients, the least squares method was modified using past inputs to estimate a value. The method explained in this article was evaluated in 5 experiments using actual flight data from the aircraft. Finally, the maximum estimation error generated by the modified method is 6.7%, which was related to the pitching moment coefficient.

In this paper, a meshless approach utilizing least-squares error technique and Taylor series was used to numerically solve an inviscid hypersonic flow. Second and fourth order derivatives were used as artificial dissipation terms to stabilize the solution and prevent unwanted oscillations especially around the vicinity of shockwave. In this study, chemical reactions caused by increased temperature were assumed to be in equilibrium condition and derived graphs were used to estimate the specific heat ratio. We used an explicit four-stage Runge–Kutta method for temporal discretization of governing equations, and used local time-stepping and residual smoothing techniques to accelerate the convergence process. The results obtained from meshless approach were compared with those obtained from finite-volume method with identical point distribution, and this comparison showed that using meshless approach provides better convergence and lower computation time. Result also showed that replacing ideal gas model with real gas model and applying the hot gas effects lead to precise identification of shockwave’s location, and provides a more accurate prediction of temperature and pressure distribution behind the shockwave.

Dam break time history have always been the intrest of many researchers. This phenomena can be modeled by Eulerian or Lagrangian approach which each of them have their benefits and disadvantages. In this paper isogeometric method is utilized for modeling flow in dam break analysis by Lagrangian approach. Mass and momentum conservation laws are governing equations of flow which are solved by pressure correction in Lagrangian approach. Least square method is used for discretization of space. Matrix size is notably smaller in isogeometric method in comparison with other methods (finite elements and meshless methods). Also stiffness matrix is symmetric and positive definitive. NURBS (Non - Uniform Rational B - Spline) functions are used as shape functions. Free surface profile and pressure values of isogeometric method in different times are compared with a meshless method. The results indicate the ability of the proposed method in solution of moving fluid with moving boundaries.