Search results

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a ‘virtual world’ populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.

The purpose of the paper is to present a method for efficiently obtaining the steady‐state solution of the quasi‐static Maxwell's equations in case of nonlinear material properties and periodic excitations.

The fixed‐point method is used to take account of the nonlinearity of the material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all nonlinear iterations. Owing to the application of the fixed‐point technique the harmonics are decoupled. The optimal parameter of the fixed‐point method is determined to accelerate its convergence speed. It is shown how this algorithm works with iterative linear equation solvers.

The optimal parameter of the fixed‐point method is determined and it is also shown how this method works if the equation systems are solved iteratively.

The convergence criterion of the iterative linear equation solver is determined. The method is used to solve three‐dimensional problems.

The purpose of this paper is to numerically solve Eikonal and Hamilton‐Jacobi equations using the finite element method; to use both explicit Taylor Galerkin (TG) and implicit methods to obtain shortest wall distances; to demonstrate the implemented methods on some realistic problems; and to use iterative generalized minimal residual method (GMRES) method in the solution of the equations.

The finite element method along with both the explicit and implicit time discretisations is employed. Two different forms of governing equations are also employed in the solution. The Eikonal equation in its original form is used in the explicit Taylor Galerkin discretisation to save computational time. For implicit method, however, the convection‐diffusion form in its conservation form is used to maintain spatial stability.

The finite element solution obtained is both accurate and smooth. As expected the implicit method is much faster than the explicit method. Though the proposed finite element solution procedures in serial is slower than the standard search procedure, they are suitable to be used in a parallel environment.

The finite element procedure for Eikonal and Hamilton‐Jacobi equations are attempted for the first time. Though the finite volume and finite difference‐based computational fluid dynamics (CFD) solvers have started employing differential equations for wall distance calculations, it is not common for finite element solvers to use such wall distance calculations. The results presented here clearly show that the proposed methods are suitable for unstructured meshes and finite element solvers.

The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures.

The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model.

A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion.

One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

The purpose of this paper is to describe a novel universal error estimator and the adaptive time-stepping process in the generalized single-step single-solve (GS4-1) computational framework, applied for the fluid dynamics with illustrations to incompressible Navier–Stokes equations.

The proposed error estimator is universal and versatile that it works for the entire subsets of the GS4-1 framework, encompassing the nondissipative Crank–Nicolson method, the most dissipative backward differential formula and anything in between. It is new and novel that the cumbersome design work of error estimation for specific time integration algorithms can be avoided. Regarding the numerical implementation, the local error estimation has a compact representation that it is determined by the time derivative variables at four successive time levels and only involves vector operations, which is simple for numerical implementation. Additionally, the adaptive time-stepping is further illustrated by the proposed error estimator and is used to solve the benchmark problems of lid-driven cavity and flow past a cylinder.

The proposed computational procedure is capable of eliminating the nonphysical oscillations in GS4-1(1,1)/Crank–Nicolson method; being CPU-efficient in both dissipative and nondissipative schemes with better solution accuracy; and detecting the complex physics and hence selecting a suitable time step according to the user-defined error threshold.

To the best of the authors’ knowledge, for the first time, this study applies the general purpose GS4-1 family of time integration algorithms for transient simulations of incompressible Navier–Stokes equations in fluid dynamics with constant and adaptive time steps via a novel and universal error estimator. The proposed computational framework is simple for numerical implementation and the time step selection based on the proposed error estimation is efficient, benefiting to the computational expense for transient simulations.

To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.

The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge‐Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.

Standard error‐controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.

Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.

To develop an effective and reliable procedure for the calculation of heat fluxes from the measured temperatures in experimental tests of impingement water cooling.

An inverse heat transfer analysis procedure is developed and implemented into a 2D finite element program. In this method, the least‐squares technique, sequential function specification and regularization are used. Simplifications in the sensitivity matrix calculation and iterative procedures are introduced. The triangular and impulse‐like profiles of heat fluxes simulating practical conditions of impingement water cooling are used to investigate the accuracy and stability of the proposed inverse procedure. The developed program is then used to determine the heat flux during impingement water cooling.

A hybrid procedure is developed in which inverse calculations are conducted with a computation window. This procedure may be used as a whole time domain method or become a periodically sequential or real sequential method by adjusting the sequential steps.

Parametric study and application show that the developed method is effective and reliable and that inverse analysis may obtain the heat flux with an acceptable level of accuracy.

This paper aims to describe a research effort towards the comprehension of the unsteady phenomena due to the deployment of high-lift devices at approach/landing conditions.

The work starts from a preexisting platform based on an immersed boundary (IB) method whose capabilities are extended to study compressible and viscous flows around moving/deforming objects. A hybrid Lagrangian-Eulerian approach is designed to consider the motion of multiple bodies through a fixed Cartesian mesh. That is, the cells’ volumes do not move in space but rather they observe the solid walls crossing themselves. A dynamic discrete forcing makes use of a moving least-square procedure which has been validated by simulating well-known benchmarks available for rigid body motions. Partitioned fluid-structure interactions (FSI) strategies are explored to consider aeroelastic phenomena. A shared platform, between the aerodynamic and the structural solvers, fulfils the loads’ transfer and drives the sequence of the operating steps.

The first part of the results is devoted to a basic two-dimensional study aiming at evaluating the accuracy of the method when simple rigid motions are prescribed. Afterwards, the paper discusses the solution obtained when applying the dynamic IB method to the rigid deployment of a Krueger-flap. The final section discusses the aeroelastic behaviour of a three-element airfoil during its deployment phase. A loose FSI coupling is applied for estimating the possible loads’ downgrade.

The IB surfaces are allowed to move less than one IB-cell size at each time-step de-facto restricting the Courant-Friedrichs-Lewy (CFL) based on the wall velocity to be smaller than unity. The violation of this constraint would impair the explicit character of the method.

The proposed method improves automation in FSI numerical analysis and relaxes the human expertise/effort for meshing the computational domain around complex three-dimensional geometries. The logical consequence is an overall speed-up of the simulation process.

The value of the paper consists in demonstrating the applicability of dynamic IB techniques for studying high-lift devices. In particular, the proposed Cartesian method does not want to compete with body-conforming ones whose accuracy remains generally superior. Rather, the merit of this research is to propose a fast and automatic simulation system as a viable alternative to classic multi-block structured, chimaera or unstructured tools.

The purpose of this study is to demonstrate that using appropriate values for fictitious parameters is very important in dynamic relation methods. It will be shown that a better scheme can be made by modifying these terms.

Former research studies have proposed diverse values for fictitious parameters. These factors are very essential and highly affect structural analyses’ abilities. In this paper, the fictitious masses in ten previous well-known schemes are replaced with each other. These formulations lead to the extra 41 different new procedures.

To compare the skills of the created processes with those of the ten previous ones, 14 benchmark problems with geometrical nonlinear behaviour are analysed. The performances’ evaluations are based on the number of iterations and analysis time. Considering these two criteria, the score of each technique is found for the ranking assessments.

To solve a static problem by using a dynamic relaxation (DR) scheme, it should be first converted to a dynamic space. Using the appropriate values for fictitious terms is very important in this approach. The fictitious mass matrix and damping factor play the most effective role in the process stability. Besides, the fictitious time step is necessary for improving the method convergence rate.

Different famous DR procedures were compared with each other previously. These solvers used their original assumptions for the imaginary mass and damping. So far, no attempt has been made to change the fictitious parameters of the well-known DR methods. As these fictitious factors highly affect structural analyses’ efficiencies, these solvers are formulated again by using new parameters. In this study, the fictitious masses of ten previous famous methods are replaced with each other. These substitutions give 51 different procedures.

It is concluded that the present formulations lead to more effective and favourable methods than the solvers with previous assumptions.