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Article
Publication date: 7 March 2016

Rhodri LT Bevan and P Nithiarasu

In the present work, a novel dual time stepping approach is applied to a quasi-implicit (QI) fractional step method and its performance is assessed against the classical versions…

Abstract

Purpose

In the present work, a novel dual time stepping approach is applied to a quasi-implicit (QI) fractional step method and its performance is assessed against the classical versions of the QI procedure for the solution of incompressible Navier-Stokes equations. The paper aims to discuss these issues.

Design/methodology/approach

In the proposed method, a local time stepping algorithm is utilised to accelerate the solution to steady state, while the transient solution is recovered through the use of a dual time step. It is demonstrated that, unlike the classical fractional step method, the temporal convergence rate of the proposed method depends solely upon the choice of the time discretisation.

Findings

While additional stabilisation is the prerequisite for obtaining higher order accuracy in the standard QI methods, the proposed dual time stepping approach completely eliminates this requirement. In addition, the dual time stepping approach proposed achieves the correct formal accuracy in time for both velocity and pressure. It is also demonstrated that a time accuracy beyond second order for both pressure and velocity is possible. In summary, the proposed dual time approach to QI methods simplifies the algorithm, accelerates solution and achieves a higher order time accuracy.

Originality/value

The dual time stepping removed first order pressure error.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 November 2018

Nikhil Kalkote, Ashwani Assam and Vinayak Eswaran

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

243

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 October 2019

Lisha He, Jianjing Zheng, Yao Zheng, Jianjun Chen, Xuan Zhou and Zhoufang Xiao

The purpose of this paper is to develop parallel algorithms for moving boundary simulations by local remeshing and compose them to a fully parallel simulation cycle for the…

Abstract

Purpose

The purpose of this paper is to develop parallel algorithms for moving boundary simulations by local remeshing and compose them to a fully parallel simulation cycle for the solution of problems with engineering interests.

Design/methodology/approach

The moving boundary problems are solved by unsteady flow computations coupled with six-degrees-of-freedom equations of rigid body motion. Parallel algorithms are developed for both computational fluid dynamics (CFD) solution and grid deformation steps. Meanwhile, a novel approach is developed for the parallelization of the local remeshing step. It inputs a distributed mesh after deformation, then marks low-quality elements to be deleted on the respective processors. After that, a parallel domain decomposition approach is used to repartition the hole mesh and then to redistribute the resulting sub-meshes onto all available processors. Then remesh individual sub-holes in parallel. Finally, the element redistribution is rebalanced.

Findings

If the CFD solver is parallelized while the remaining steps are executed in sequential, the performance bottleneck of such a simulation cycle is observed when the simulation of large-scale problem is executed. The developed parallel simulation cycle, in which all of time-consuming steps have been efficiently parallelized, could overcome these bottlenecks, in terms of both memory consumption and computing efficiency.

Originality/value

A fully parallel approach for moving boundary simulations by local remeshing is developed to solve large-scale problems. In the algorithm level, a novel parallel local remeshing algorithm is present. It repartitions distributed hole elements evenly onto all available processors and ensures the generation of a well-shaped inter-hole boundary always. Therefore, the subsequent remeshing step can fix the inter-hole boundary involves no communications.

Details

Engineering Computations, vol. 36 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1997

S. Sundarraj and V.R. Voller

Explains that segregation processes during the solidification of a binary alloy occur at two distinct length scales: on the microscopic length scale of the crystal interface, in…

3062

Abstract

Explains that segregation processes during the solidification of a binary alloy occur at two distinct length scales: on the microscopic length scale of the crystal interface, in the two‐phase mushy zone, segregation is controlled by solid state mass diffusion; and, on the macroscopic scale of the process, segregation is controlled by the convective transport of the molten metal. Concludes that developing models that can capture both these scales is a challenge. Introduces a bi‐level grid, and uses a macro grid on the scale of the process for the solution of equations describing macroscopic heat and mass transport. Details how each node point in the macro grid is associated with a micro grid on which equations describing the microscopic phenomena in the mushy region are solved. In this way, develops a dual‐scale model of segregation during the solidification of a binary alloy. On investigating the unidirectional solidification of a binary alloy, demonstrates that this dual‐scale model is able to capture both the macro and micro‐scales in a single numerical treatment.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 2/3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 May 2016

Nicola Massarotti, Michela Ciccolella, Gino Cortellessa and Alessandro Mauro

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the…

Abstract

Purpose

The purpose of this paper is to focus on the numerical analysis of transient free convection heat transfer in partially porous cylindrical domains. The authors analyze the dependence of velocity and temperature fields on the geometry, by analyzing transient flow behavior for different values of cavity aspect ratio and radii ratio; both inner and outer radius are assumed variable in order to not change the difference ro-ri. Moreover, several Darcy numbers have been considered.

Design/methodology/approach

A dual time-stepping procedure based on the transient artificial compressibility version of the characteristic-based split algorithm has been adopted in order to solve the transient equations of the generalized model for heat and fluid flow through porous media. The present model has been validated against experimental data available in the scientific literature for two different problems, steady-state free convection in a porous annulus and transient natural convection in a porous cylinder, showing an excellent agreement.

Findings

For vertically divided half porous cavities, with Rayleigh numbers equal to 3.4×106 for the 4:1 cavity and 3.4×105 for the 8:1 cavity, the numerical results show that transient oscillations tend to disappear in presence of cylindrical geometry, differently from what happens for rectangular one. The magnitude of this phenomenon increases with radii ratio; the porous layer also affects the stability of velocity and temperature fields, as oscillations tend to decrease in presence of a porous matrix with lower value of the Darcy number.

Research limitations/implications

A proper analysis of partially porous annular cavities is fundamental for the correct estimation of Nusselt numbers, as the formulas provided for rectangular domains are not able to describe these problems.

Practical implications

The proposed model represents a useful tool for the study of transient natural convection problems in porous and partially porous cylindrical and annular cavities, typical of many engineering applications. Moreover, a fully explicit scheme reduces the computational costs and ensures flexibility.

Originality/value

This is the first time that a fully explicit finite element scheme is employed for the solution of transient natural convection in partially porous tall annular cavities.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 March 2017

Tianyu Lu, Juanmian Lei, Xiaosheng Wu and Jintao Yin

The purpose of this paper is to examine the ability of the harmonic balance method for predicting the aerodynamic characteristics of rigid finned spinning vehicle.

230

Abstract

Purpose

The purpose of this paper is to examine the ability of the harmonic balance method for predicting the aerodynamic characteristics of rigid finned spinning vehicle.

Design/methodology/approach

The aerodynamic characteristics of a rigid four-finned spinning vehicle at Mach number 2.5 and angle of attack of 20 degrees are simulated using the harmonic balance method and the unsteady time-accurate approach based on the dual-time method. The numerical results are analyzed, and the computed aerodynamic coefficients of the harmonic balance method are compared with those of the dual-time method. The influence of the number of harmonics is presented. The computed Magnus force and moment coefficients are compared with the experimental data. The flow fields at different roll angles are presented. The computational efficiency of harmonic balance method is analyzed.

Findings

The results show that the aerodynamic coefficients of spinning vehicle could be predicted by the harmonic balance method with reasonable accuracy compared with the dual-time method. For the harmonic balance method, the accuracy of the computed leeward side flow is relatively poor compared with that of the computed windward side flow. Meanwhile, the computational efficiency is influenced by initial guess and the intensity of unsteady effect.

Practical implications

The harmonic balance method could be used for the aerodynamic prediction of spinning vehicle, which may improve the efficiency of vehicle design.

Originality/value

This paper presents the results of the harmonic balance method for simulating the aerodynamic characteristics of finned spinning vehicle. The accuracy and efficiency of the method are analyzed.

Details

Aircraft Engineering and Aerospace Technology, vol. 89 no. 2
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 1 June 2001

P. De Palma, G. Pascazio and M. Napolitano

This paper describes two accurate and efficient numerical methods for computing unsteady viscous flows. The first one solves the incompressible Navier‐Stokes equations in their…

Abstract

This paper describes two accurate and efficient numerical methods for computing unsteady viscous flows. The first one solves the incompressible Navier‐Stokes equations in their vorticity‐velocity formulation, using a staggered‐grid finite‐volume spatial discretization to provide second‐order accuracy on arbitrary grids, and combines effectively an alternating direction implicit scheme for the vorticity transport equation and a multigrid line‐Gauss‐Seidel relaxation for the velocity equations. The second method solves the compressible Reynolds‐averaged Navier‐Stokes equations in strong conservation form, with a k−ω turbulence closure model. The equations are discretized in time using an implicit three‐time‐level scheme, combined with a dual time stepping approach, so that the residual at every physical time step is annihilated using an efficient multigrid Runge‐Kutta iteration with variable time stepping and implicit residual smoothing. The space discretization uses a Roe’s flux difference splitting for the convective terms and standard central differences for the diffusive ones. A turbulent unsteady cascade flow is used to demonstrate the accuracy and efficiency of the method. The authors are currently working towards extending the two approaches described in this paper to three space dimensions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 11 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 May 2016

Rhodri LT Bevan, Etienne Boileau, Raoul van Loon, R.W. Lewis and P Nithiarasu

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not…

Abstract

Purpose

The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared.

Design/methodology/approach

This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split.

Findings

In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations.

Originality/value

A comprehensive comparison between three versions of the CBS method is provided for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 2003

M.T. Manzari

A finite element solution procedure is presented for the simulation of transient incompressible fluid flows using triangular meshes. The algorithm is based on the artificial…

1328

Abstract

A finite element solution procedure is presented for the simulation of transient incompressible fluid flows using triangular meshes. The algorithm is based on the artificial compressibility technique in connection with a dual timestepping approach. A second‐order discretization is employed to achieve the required accuracy in real‐time while an explicit multistage Runge‐Kutta scheme is used to march in the pseudo‐time domain. A standard Galerkin finite element method, stabilized by using an artificial dissipation technique, is used for the spatial discretization. The performance of the proposed algorithm is demonstrated by solving a set of internal and external problems including flows with purely transient and periodic behavior.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 July 2015

He-yong Xu, Shi-long Xing and Zheng-yin Ye

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around…

Abstract

Purpose

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around rotational parts of aircraft.

Design/methodology/approach

The computational domain is decomposed into two sub-domains, namely, the rotational sub-domain which contains the rotational boundaries, and the stationary sub-domain which contains the remainder flow field including the stationary boundaries. The artificial boundaries and restriction boundaries are used as the restriction condition to generate the entire computational grid, and then the overset grids are established according to the radius parameters of artificial boundaries set previously. The deformation of rotational boundary is treated by using the linear spring analogy method which is suitable for the dynamic unstructured grid. The unsteady Navier-Stokes/Euler equations are solved separately in the rotational sub-domain and stationary sub-domain, and data coupling is accomplished through the overlapping area. The least squares method is used to interpolate the flow variables for the artificial boundary points with a higher calculating precision. Implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) time stepping scheme is implemented to accelerate the inner iteration during the unsteady simulation.

Findings

The airfoil steady flow, airfoil pitching unsteady flow, three-dimensional (3-D) rotor flow field, rotor-fuselage interaction unsteady flow field and the flutter exciting system unsteady flow field are numerically simulated, and the results have good agreements with the experimental data. It is shown that the present method is valid and efficient for the prediction of complicated unsteady problems which contain rotational dynamic boundaries.

Research limitations/implications

The results are entirely based on computational fluid dynamics (CFD), and the 3D simulations are based on the Euler equations in which the viscous effect is ignored. The current work shows further applicable potential to simulate unsteady flow around rotational parts of aircraft.

Practical implications

The current study can be used to simulate the two-dimensional airfoil pitching, 3-D rotor flow field, rotor-fuselage interaction and the flutter exciting system unsteady flow. The work will help the aircraft designer to get the unsteady flow character around rotational parts of aircraft.

Originality/value

A new type of rotational dynamic overset grids is presented and validated, and the current work has a significant contribution to the development of unstructured rotational dynamic overset grids.

Details

Aircraft Engineering and Aerospace Technology: An International Journal, vol. 87 no. 4
Type: Research Article
ISSN: 0002-2667

Keywords

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