Search results

This paper aims to provide a simple and accurate higher order predictor‐corrector integration which can be used in dynamic analysis and to compare it with the previous works.

The predictor‐corrector integration is defined by combining the higher order explicit and implicit integrations in which displacement and velocity are assumed to be functions of accelerations of several previous time steps. By studying the accuracy and stability conditions, the weighted factors and acceptable time step are determined.

Simplicity and vector operations plus accuracy and stability are the main specifications of the new predictor‐corrector method. This procedure can be used in linear and nonlinear dynamic analysis.

In the proposed integration, time step is assumed to be constant.

The numerical integration is the heart of a dynamic analysis. The result's accuracy is strongly influenced by the accuracy and stability of the numerical integration.

This paper presents simple and accurate predictor‐corrector integration based on accelerations of several previous time steps. This may be used as a routine in any dynamic analysis software to enhance accuracy and reduce computational time.

The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

The proposed approaches build on a method developed by the authors involving Padé approximates about each function sample. Both single‐ and multi‐step methods are suggested. The use of Richardson extrapolation is recommended for increasing efficiency.

The efficacy of the methods is shown using two examples and results are compared to a standard integration technique.

The paper shows that the methods are suitable for application in any field of science requiring efficient and accurate numerical solution of stiff differential equations.

The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces.

In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics.

Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability.

The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.

Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations.

Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes.

It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall cavity. In all the cases the results agree very well with exemplary solutions.

A staggered or half-staggered grid arrangement is usually used for the projection method for both constant and low Mach number flows. The staggered approach ensures stability and strong pressure-velocity coupling. In the paper a high-order compact method has been implemented in the framework of low Mach number approximation on collocated meshes. The resulting algorithm is accurate, robust for large density variations and is almost free from the pressure oscillations.

The aim of this study is to design a guidance method to generate a smoother and feasible gliding reentry trajectory, a highly constrained problem by formalizing the control variables profile.

A novel accelerated fractional-order particle swarm optimization (FAPSO) method is proposed for velocity updates to design the guidance method for gliding reentry flight vehicles with fixed final energy.

By using the common aero vehicle as a test case for the simulation purpose, it is found that during the initial phase of the longitudinal guidance, there are oscillations in the state parameters which cause to violate the path constraints. For the glide phase of the longitudinal guidance, the path constraints have higher values because of the increase in the atmosphere density.

The violation in the path constraints may compromise the flight vehicle safety, whereas the enforcement assures the flight safety by flying it within the reentry corridor.

An oscillation suppression scheme is proposed by using the FAPSO method during the initial phase of the reentry flight, which smooths the trajectory and enforces the path constraints partially. To enforce the path constraints strictly in the glide phase, ultimately, another scheme by using the FAPSO method is proposed. The simulation results show that the proposed algorithm is efficient to achieve better convergence and accuracy for nominal as well as dispersed conditions.

The purpose of this paper is to develop a block method of order five for the general solution of the first-order initial value problems for Volterra integro-differential equations (VIDEs).

A collocation approximation method is adopted using the shifted Legendre polynomial as the basis function, and the developed method is applied as simultaneous integrators on the first-order VIDEs.

The new block method possessed the desirable feature of the Runge–Kutta method of being self-starting, hence eliminating the use of predictors.

In this paper, some information about solving VIDEs is provided. The authors have presented and illustrated the collocation approximation method using the shifted Legendre polynomial as the basis function to investigate solving an initial value problem in the class of VIDEs, which are very difficult, if not impossible, to solve analytically. With the block approach, the non-self-starting nature associated with the predictor corrector method has been eliminated. Unlike the approach in the predictor corrector method where additional equations are supplied from a different formulation, all the additional equations are from the same continuous formulation which shows the beauty of the method. However, the absolute stability region showed that the method is A-stable, and the application of this method to practical problems revealed that the method is more accurate than earlier methods.

In this contribution, the solution of Mass-Spring-Damper Systems in the fractional context by using Caputo derivative and Orthogonal Collocation Method is investigated. For this purpose, different case studies considering constant and periodic sources are evaluated. The dimensional consistency of the model is guaranteed by introducing an auxiliary parameter. The obtained results are compared with those found by using both the analytical solution and the predictor-corrector method of Adams–Bashforth–Moulton type. The influence of the fractional order on the mechanical system is evaluated.

In the present contribution, an extension of the Orthogonal Collocation Method to solve fractional differential equations is proposed.

In general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics.

The development of a new numerical method to solve fractional differential equations is the major contribution.

When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis.

In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder.

The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori.

Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

Considers hysteretic non‐linear models for modelling horizontal force‐displacement characteristics of an isolation system subjected to general plane motion. Simple close form solution of the stiff differential equation of hysteretic model for forces mobilized in the non‐linear elements of the base isolation system are obtained. Simulates experimental shear force‐displacement loops obtained from the bi‐axial tests by different investigators. Both the experimental and the simulated hysteresis loops are found to be in good agreement. Develops a unified solution algorithm for computation of response of different types of base isolated buildings, considering non‐linear behaviour of the isolation systems, subjected to multi‐directional motion. The solution algorithm is based on the implicit‐implicit partitioned Newmark’s method in predictor‐corrector form. Response of the base isolated symmetrical building as obtained from the solution algorithm and the computer programs developed are in good agreement with that obtained from the more complex numerical studies reported in the literature. Response of a three storeyed symmetrical building isolated by pure friction isolators and laminated rubber bearings has been obtained using this simple yet accurate solution algorithm.

This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles.

A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate.

A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity.

Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces.

The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.