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Journal articles on the topic 'Dual Time Stepping'

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Author: Grafiati

Published: 10 March 2023

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1

Nordström, Jan, and Andrea A. Ruggiu. "Dual Time-Stepping Using Second Derivatives." Journal of Scientific Computing 81, no. 2 (September 9, 2019): 1050–71. http://dx.doi.org/10.1007/s10915-019-01047-5.

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Abstract We present a modified formulation of the dual time-stepping technique which makes use of two derivatives in pseudo-time. This new technique retains and improves the convergence properties to the stationary solution. When compared with the conventional dual time-stepping, the method with two derivatives reduces the stiffness of the problem and requires fewer iterations for full convergence to steady-state. In the current formulation, these positive effects require that an approximation of the square root of the spatial operator is available and inexpensive.

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2

Elmahi, I., O. Gloth, D. Hänel, and R. Vilsmeier. "A preconditioned dual time-stepping method for combustion problems." International Journal of Computational Fluid Dynamics 22, no. 3 (March 2008): 169–81. http://dx.doi.org/10.1080/10618560701833333.

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3

Parent, Bernard. "Positivity-preserving dual time stepping schemes for gas dynamics." Journal of Computational Physics 361 (May 2018): 391–411. http://dx.doi.org/10.1016/j.jcp.2018.01.046.

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4

Wright, Rachel L., Afia Masood, Elinor S. MacCormac, David Pratt, Catherine M. Sackley, and Alan M. Wing. "Metronome-Cued Stepping in Place after Hemiparetic Stroke: Comparison of a One- and Two-Tone Beat." ISRN Rehabilitation 2013 (November 17, 2013): 1–5. http://dx.doi.org/10.1155/2013/157410.

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Hemiparetic gait is characterised by temporal asymmetry and variability, and these variables are improved by auditory cueing. Stepping in place incorporates aspects of gait and may be a useful tool for locomotor training. The aim of this pilot study was to investigate the use of a single-tone and dual-tone metronome to cue stepping in place after hemiparetic stroke. Eight participants completed an uncued baseline stepping condition and two cued stepping conditions utilising a single-tone and a dual-tone metronome. Step times were determined from force plate data, and asymmetry and variability were calculated for the three conditions. Step time asymmetry was significantly reduced in the single-tone condition compared to baseline, and paretic step time variability was significantly reduced in both cued conditions. The single-tone metronome appeared to be preferred to the dual-tone metronome based on participant feedback. The results of this pilot study suggest that metronome cueing produces similar benefits on stepping in place to previously reported findings in walking. Further research on whether stepping in place to a metronome can be used for locomotor training is needed.

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5

Stepp, Willi L., and Zeynep Ökten. "Resolving kinesin stepping: one head at a time." Life Science Alliance 2, no. 5 (October 2019): e201900456. http://dx.doi.org/10.26508/lsa.201900456.

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Kinesins are well known to power diverse long-range transport processes in virtually all eukaryotic cells. The ATP-dependent processive stepping as well as the regulation of kinesin’ activity have, thus, been the focus of extensive studies over the past decades. It is widely accepted that kinesin motors can self-regulate their activity by suppressing the catalytic activity of the “heads.” The distal random coil at the C terminus, termed “tail domain,” is proposed to mediate this autoinhibition; however, a direct regulatory influence of the tail on the processive stepping of kinesin proved difficult to capture. Here, we simultaneously tracked the two distinct head domains in the kinesin-2 motor using dual-color super resolution microscopy (dcFIONA) and reveal for the first time their individual properties during processive stepping. We show that the autoinhibitory wild-type conformation selectively impacts one head in the heterodimer but not the other. Our results provide insights into the regulated kinesin stepping that had escaped experimental scrutiny so far.

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6

Kalkote, Nikhil, Ashwani Assam, and Vinayak Eswaran. "Towards developing an adaptive time stepping for compressible unsteady flows." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 2 (February 4, 2019): 487–503. http://dx.doi.org/10.1108/hff-03-2018-0095.

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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.

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7

Harada, Nobuko, Shuichi Okada, and Shinya Negoro. "Age-Related Differences in Stepping Response When Stepping onto a Known Soft Surface under Dual Task Conditions." Current Gerontology and Geriatrics Research 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/701897.

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The purpose of this study was to investigate whether age-related differences in stepping response influence postural control when stepping onto a known soft surface under dual task conditions. Nine young and eleven older female adults participated. First, they stepped on a flat surface while grasping an empty cup (single task), and then they repeated the task while grasping a cup filled with water (dual task). For the second experiment, they stepped on a soft surface placed in front of them while performing the above tasks. The main result was that %DIP (initiation phase as a percentage of the total stepping task time) was significantly higher for older than for young adults during the dual task on the soft surface. In conclusion, caution due to previous experience may increase attentional demand during dual tasks and lengthen the time required for central nervous processing in order to avoid losing postural stability in older adults, resulting in reductions in step velocity and step length compared to those in young adults.

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8

de Jouëtte, C., O. Laget, J. M. Le Gouez, and H. Viviand. "A dual time stepping method for fluid–structure interaction problems." Computers & Fluids 31, no. 4-7 (May 2002): 509–37. http://dx.doi.org/10.1016/s0045-7930(01)00068-8.

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9

Shan, Li, Jiangyong Hou, Wenjing Yan, and Jie Chen. "Partitioned Time Stepping Method for a Dual-Porosity-Stokes Model." Journal of Scientific Computing 79, no. 1 (November 30, 2018): 389–413. http://dx.doi.org/10.1007/s10915-018-0879-3.

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10

Zhang, Chi, Massoud Rezavand, and Xiangyu Hu. "Dual-criteria time stepping for weakly compressible smoothed particle hydrodynamics." Journal of Computational Physics 404 (March 2020): 109135. http://dx.doi.org/10.1016/j.jcp.2019.109135.

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11

Chan, Wing-Nga, and William Wai-Nam Tsang. "Effect of Tai Chi Training on Dual-Tasking Performance That Involves Stepping Down among Stroke Survivors: A Pilot Study." Evidence-Based Complementary and Alternative Medicine 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/9134173.

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Descending stairs demands attention and neuromuscular control, especially with dual-tasking. Studies have demonstrated that stroke often degrades a survivor’s ability to descend stairs. Tai Chi has been shown to improve dual-tasking performance of healthy older adults, but no such study has been conducted in stroke survivors. This study investigated the effect of Tai Chi training on dual-tasking performance that involved stepping down and compared it with that of conventional exercise among stroke survivors. Subjects were randomized into Tai Chi (n=9), conventional exercise (n=8), and control (n=9) groups. Those in the former two groups received 12-week training. Assessments included auditory Stroop test, stepping down test, and dual-tasking test involving both simultaneously. They were evaluated before training (time-1), after training (time-2), and one month after training (time-3). Tai Chi group showed significant improvement in the auditory Stroop test from time-1 to time-3 and the performance was significantly better than that of the conventional exercise group in time-3. No significant effect was found in the stepping down task or dual-tasking in the control group. These results suggest a beneficial effect of Tai Chi training on cognition among stroke survivors without compromising physical task performance in dual-tasking. The effect was better than the conventional exercise group. Nevertheless, further research with a larger sample is warranted.

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12

Shi, Yong Qiang, Qing Zhen Yang, and Xin Hai Zhou. "Application of Harmonic Balance Method to Numerical Model Unsteady Viscous Flow around Oscillating Cascade." Applied Mechanics and Materials 50-51 (February 2011): 583–88. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.583.

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A harmonic balance approach has been developed to compute nonlinear viscous unsteady flows around oscillating blades. The computed results using two orders harmonic balance method are compared with those by conventional dual-time stepping method. Results obtained with the present method agree well with those from dual-time stepping method, which demonstrate the ability of the present analysis method to model accurately the unsteady flow. Furthermore，the present method is highly efficient. It is about 36 times fast than conventional dual-time stepping method in the present computation. Then the effects of oscillation amplitude and reduced frequency on unsteadiness of flows are studied. The analysis exploits the fact that, (1) the hysteresis effect of unsteady flow is hardly affected by oscillation amplitude, but the first harmonic unsteady pressure across the blade is proportional to oscillation amplitude; (2) the higher the reduced frequency, the wider the range of unsteady aerodynamic forces, the more intense the hysteresis effect.

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13

Yi, Tae-Hyeong. "Time integration of unsteady nonhydrostatic equations with dual time stepping and multigrid methods." Journal of Computational Physics 374 (December 2018): 873–92. http://dx.doi.org/10.1016/j.jcp.2018.08.003.

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14

Meidner, Dominik, and Thomas Richter. "Goal-Oriented Error Estimation for the Fractional Step Theta Scheme." Computational Methods in Applied Mathematics 14, no. 2 (April 1, 2014): 203–30. http://dx.doi.org/10.1515/cmam-2014-0002.

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Abstract. In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, by combining three substeps of the theta time-stepping scheme, the fractional step theta time-stepping scheme is derived. It possesses highly desired stability and numerical dissipation properties and is second order accurate. The derived error estimator is based on a Petrov–Galerkin formulation that is up to a numerical quadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled as one weighted residual term given by the dual weighted residual method and one additional residual estimating the Galerkin error between time-stepping scheme and Petrov–Galerkin formulation.

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15

DeRango, S., and D. W. Zingg. "Improvements to a Dual-Time-Stepping Method for Computing Unsteady Flows." AIAA Journal 35, no. 9 (September 1997): 1548–50. http://dx.doi.org/10.2514/2.7485.

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16

Low, Chee Meng, Eddie Yin-Kwee Ng, Srikanth Narasimalu, Kie Hian Chua, and Youngkook Kim. "Adaptive discretisation and dual-rate time-stepping of mooring cable dynamics." Ocean Engineering 188 (September 2019): 106275. http://dx.doi.org/10.1016/j.oceaneng.2019.106275.

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17

DeRango, S., and D. W. Zingg. "Improvements to a dual-time-stepping method for computating unsteady flows." AIAA Journal 35 (January 1997): 1548–50. http://dx.doi.org/10.2514/3.13706.

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18

Balcı, Şölen, and Necdet Aslan. "Two-dimensional MHD solver by fluctuation splitting and dual time stepping." International Journal for Numerical Methods in Fluids 53, no. 10 (2007): 1585–611. http://dx.doi.org/10.1002/fld.1371.

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19

Birken, Philipp, and Antony Jameson. "Blending Dual Time Stepping and Newton-Krylov Methods for Unsteady Flows." PAMM 9, no. 1 (December 2009): 597–98. http://dx.doi.org/10.1002/pamm.200910270.

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20

Fu, Huazheng, and Xueshang Feng. "Splitting based scheme for three-dimensional MHD with dual time stepping." Chinese Journal of Space Science 35, no. 1 (2015): 9. http://dx.doi.org/10.11728/cjss2015.01.009.

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21

Xie, Fang, Wu Li Chu, Hai Xia Du, and Kai Zhou. "Investigation of Unsteady Flow in an Axial Compression Based on Double Times Dual Time Stepping." Applied Mechanics and Materials 757 (April 2015): 29–32. http://dx.doi.org/10.4028/www.scientific.net/amm.757.29.

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A numerical investigate of unsteady (rotor 37) based on dual time step is carried out .Results were used to identify the existence of an interface between the approach fluid and the tip-leakage flow. This paper discusses mechanism of spike stall.

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22

Sevilla, Ruben. "An implicit HDG method for linear convection-diffusion with dual time stepping." Journal of Computational Physics 434 (June 2021): 110201. http://dx.doi.org/10.1016/j.jcp.2021.110201.

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23

Chassaing, J. C., G. A. Gerolymos, and I. Vallet. "Reynolds-Stress Model Dual-Time-Stepping Computation of Unsteady Three-Dimensional Flows." AIAA Journal 41, no. 10 (October 2003): 1882–94. http://dx.doi.org/10.2514/2.1904.

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24

Liu, Yi, Gang Wang, and Zhengyin Ye. "Dynamic mode extrapolation to improve the efficiency of dual time stepping method." Journal of Computational Physics 352 (January 2018): 190–212. http://dx.doi.org/10.1016/j.jcp.2017.09.043.

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25

Breuer, M., and D. Hänel. "A dual time-stepping method for 3-d, viscous, incompressible vortex flows." Computers & Fluids 22, no. 4-5 (July 1993): 467–84. http://dx.doi.org/10.1016/0045-7930(93)90020-a.

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26

Xiao, Yilong, Ethan J. Kubatko, and Colton J. Conroy. "A one-dimensional local discontinuous Galerkin Richards’ equation solution with dual-time stepping." Computational Geosciences 26, no. 1 (December 3, 2021): 171–94. http://dx.doi.org/10.1007/s10596-021-10098-3.

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27

Arnone, Andrea, Meng-Sing Liou, and Louis A. Povinelli. "Integration of Navier-Stokes equations using dual time stepping and a multigrid method." AIAA Journal 33, no. 6 (June 1995): 985–90. http://dx.doi.org/10.2514/3.12518.

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28

TANAKA, Masataka, Toshiro MATSUMOTO, and Keiji HARA. "A TIME-STEPPING DUAL RECIPROCITY BEM FOR TRANSIENT HEAT CONDUCTION IN ANISOTROPIC SOLIDS." Proceedings of The Computational Mechanics Conference 2004.17 (2004): 303–4. http://dx.doi.org/10.1299/jsmecmd.2004.17.303.

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29

Zhang, L. P., and Z. J. Wang. "A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes." Computers & Fluids 33, no. 7 (August 2004): 891–916. http://dx.doi.org/10.1016/j.compfluid.2003.10.004.

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30

Zhang, Man, and Xueshang Feng. "Implicit dual-time stepping method for a solar wind model in spherical coordinates." Computers & Fluids 115 (July 2015): 115–23. http://dx.doi.org/10.1016/j.compfluid.2015.03.020.

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31

Peles, O., and E. Turkel. "Adaptive Time Steps for Compressible Flows Based on Dual-Time Stepping and a RK/Implicit Smoother." Journal of Scientific Computing 81, no. 3 (August 7, 2019): 1409–28. http://dx.doi.org/10.1007/s10915-019-01024-y.

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32

Hassan, Oubay, Kenneth Morgan, and Nigel Weatherill. "Unstructured mesh methods for the solution of the unsteady compressible flow equations with moving boundary components." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1859 (May 22, 2007): 2531–52. http://dx.doi.org/10.1098/rsta.2007.2020.

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A review of a procedure for the simulation of time-dependent, inviscid and turbulent viscous, compressible flows involving geometries that change in time is presented. The adopted discretization technique employs unstructured meshes and both explicit and implicit time-stepping schemes. A dual time-stepping procedure and an ALE formulation enable flows involving moving boundary components to be included. Techniques that have been developed to maintain the validity of the unstructured mesh and to allow for the capture of moving flow features are also reviewed. Using the in-house developed techniques, some examples are included to demonstrate the use of the approach for the simulation of a number of flows of practical industrial interest.

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33

TIAN, SHULING, YIZHAO WU, and JIAN XIA. "NUMERICAL SIMULATION OF UNSTEADY FLOW FIELD AROUND HELICOPTER IN FORWARD FLIGHT USING A PARALLEL DYNAMIC OVERSET UNSTRUCTURED GRIDS METHOD." Modern Physics Letters B 23, no. 03 (January 30, 2009): 325–28. http://dx.doi.org/10.1142/s021798490901831x.

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A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.

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34

Nasu, Nasrin Jahan, Md Abdullah Al Mahbub, Shahid Hussain, Danping Yang, and Haibiao Zheng. "Partitioned time stepping schemes for the non-stationary dual-fracture-matrix fluid flow model." Applied Mathematical Modelling 79 (March 2020): 200–229. http://dx.doi.org/10.1016/j.apm.2019.10.032.

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35

Arnone, A., and R. Pacciani. "Rotor-Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method." Journal of Turbomachinery 118, no. 4 (October 1, 1996): 679–89. http://dx.doi.org/10.1115/1.2840923.

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A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor–stator interaction. In the proposed method, a fully implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge–Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor–stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

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36

Hoang, Phu, Daniel Schoene, Simon Gandevia, Stuart Smith, and Stephen R. Lord. "Effects of a home-based step training programme on balance, stepping, cognition and functional performance in people with multiple sclerosis – a randomized controlled trial." Multiple Sclerosis Journal 22, no. 1 (April 28, 2015): 94–103. http://dx.doi.org/10.1177/1352458515579442.

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Background: Stepping impairments increase fall risk in people with MS. No studies have evaluated step training for reducing fall risk in this population. Objectives: To determine if step training can improve physical and neuropsychological measures associated with falls in MS. Methods: 50 PwMS with moderate disability participated in a randomized controlled trial in which intervention group participants ( n = 28) performed step training for 12 weeks while controls ( n = 22) continued usual physical activity. The primary outcomes were choice stepping reaction time (CSRT) and Stroop stepping test (SST) time. Secondary outcomes included balance test (postural sway, CSRT components), gait speed and cognitive tests, nine-hole peg test (9-HPT) and MS functional composite (MSFC) score. Results: 44 participants completed the study and no adverse events were reported. Compared with the control group, the intervention group performed significantly better at retest in CSRT and SST times, and tests of sway with eyes open, 9-HPT, single and dual task gait speed and MSFC score. There was a non-significant trend for fewer falls in the intervention group. Conclusions: The findings indicate that the step training programme is feasible, safe and effective in improving stepping, standing balance, coordination and functional performance in people with MS.

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37

Guzel, Goktan, and Ilteris Koc. "Time-Accurate Flow Simulations Using a Finite-Volume Based Lattice Boltzmann Flow Solver with Dual Time Stepping Scheme." International Journal of Computational Methods 13, no. 06 (November 2, 2016): 1650035. http://dx.doi.org/10.1142/s0219876216500353.

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In this study, the Lattice Boltzmann Method (LBM) is implemented through a finite-volume approach to perform 2D, incompressible, and time-accurate fluid flow analyses on structured grids. Compared to the standard LBM (the so-called stream and collide scheme), the finite-volume approach followed in this study necessitates more computational effort, but the major limitations of the former on grid uniformity and Courant–Friedrichs–Lewy (CFL) number that is to be one are removed. Even though these improvements pave the way for the possibility of solving more practical fluid flow problems with the LBM, time-accurate simulations are still restricted due to the stability criteria dictated by high-aspect ratio grid cells that are usually required for adequate resolution of boundary layers and the stiffness due to the nature of the equation that are being solved. To overcome this limitation, a Dual Time Stepping (DTS) scheme, which iterates the solution in pseudo time using an Implicit-Explicit (IMEX) Runge–Kutta method while advancing the solution in physical time with an explicit scheme (backward difference formula), is developed and implemented. The accuracy of the resulting flow solver is evaluated using benchmark flow problems and overall second-order accuracy is demonstrated.

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38

Yu, Haijun, Guoru Huang, and Chuanhao Wu. "Efficient Finite-Volume Model for Shallow-Water Flows Using an Implicit Dual Time-Stepping Method." Journal of Hydraulic Engineering 141, no. 6 (June 2015): 04015004. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0000998.

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39

Bevan, R. L. T., and P. Nithiarasu. "Accelerating incompressible flow calculations using a quasi-implicit scheme: local and dual time stepping approaches." Computational Mechanics 50, no. 6 (September 18, 2012): 687–93. http://dx.doi.org/10.1007/s00466-012-0767-x.

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40

Zhang, Xu, and Xiu Bin He. "Numerical Simulation on Undulatory Flow of Swimming Fish." Applied Mechanics and Materials 353-356 (August 2013): 2545–49. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.2545.

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A numerical simulation is carried out to investigate the unsteady flows over a swimming fish. The three-dimensional incompressible Navier-Stokes equations are solved using the finite volume method with artificial compressibility and dual time stepping approaches on unstructured moving grid. A realistic fish-like body is modeled, which undergoes undulatory swimming in a straight line. Both inviscid and viscous flows have been simulated to study the flow structures.

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41

TANAKA, Masataka, Toshiro MATSUMOTO, and Susumu TAKAKUWA. "Dual Reciprocity Time-stepping BEM Applied to the Transient Heat Conduction Problem of Temperature-dependent Materials." Transactions of the Japan Society of Mechanical Engineers Series A 71, no. 702 (2005): 191–96. http://dx.doi.org/10.1299/kikaia.71.191.

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42

Keslerová, R., and K. Kozel. "Numerical solution of unsteady generalized Newtonian and Oldroyd-B fluids flow by dual time-stepping method." Journal of Physics: Conference Series 490 (March 11, 2014): 012111. http://dx.doi.org/10.1088/1742-6596/490/1/012111.

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43

Chen, Wenqian, Yaping Ju, and Chuhua Zhang. "A parallel inverted dual time stepping method for unsteady incompressible fluid flow and heat transfer problems." Computer Physics Communications 260 (March 2021): 107325. http://dx.doi.org/10.1016/j.cpc.2020.107325.

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44

Tanaka, Masataka, Toshiro Matsumoto, and Susumu Takakuwa. "Dual reciprocity BEM for time-stepping approach to the transient heat conduction problem in nonlinear materials." Computer Methods in Applied Mechanics and Engineering 195, no. 37-40 (July 2006): 4953–61. http://dx.doi.org/10.1016/j.cma.2005.04.025.

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45

Gaitonde, A. L., D. P. Jones, and S. P. Fiddes. "A 2D Navier-Stokes method for unsteady compressible flow calculations on moving meshes." Aeronautical Journal 102, no. 1012 (February 1998): 89–97. http://dx.doi.org/10.1017/s000192400006557x.

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AbstractA moving mesh method for the computation of compressible viscous flow past deforming and moving aerofoils is described. It is based on a well established time-marching finite-volume scheme, which has been widely used for steady compressible flows. An implicit real-time discretisation is used and the equations are integrated via a dual-time scheme. This involves the introduction of derivatives of a fictitious pseudo time. The solution at each real-time step involves seeking solutions which are steady-state solutions in pseudo time. This approach decouples the stability and accuracy limitations of the scheme and permits large real-time steps to be chosen. Also well-proven convergence acceleration techniques developed for steady flows such as local-time stepping, residual averaging and multigrid may be used in the pseudo-time stepping scheme without compromising real-time accuracy. A sequence of body-conforming grids and corresponding grid speeds is required, where the inner and outer boundaries of the grid move independently. The required grids and speeds are found using a transfinite interpolation technique. Applications of the method to external compressible flows are shown, including results from a parallel version of the computer program.

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Kumar, K. Siva, and Sharanappa V. Sajjan. "Unsteady Compressible Flow over Heaving Bodies Using an Implicit RANS Solver." Applied Mechanics and Materials 110-116 (October 2011): 4589–97. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.4589.

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Unsteady Reynolds-Averaged Navier-Stokes computations are presented for the flow over a pure plunging aerofoil and a plunging wing. The implicit RANS solver used for obtaining time-accurate solution is based on implicit finite volume nodal point spatial discretization scheme with dual time stepping. Baldwin and Lomax turbulence model has been used for the turbulence closure. The results are obtained in the form of aerodynamic coefficients, thrust coefficient and propulsion efficiency for two different cases over the aerofoil and wing and are compared with available literature.

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Xu, Yong, Guo Qing Zhang, and Fei Wang. "Investigation of the Unsteady Flow for the Supersonic Jet Element." Advanced Materials Research 201-203 (February 2011): 2178–81. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.2178.

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The unsteady viscous flow of the supersonic jet element (SJE) was simulated numerically based on CFD technology. A dual time-stepping scheme and AMG scheme were employed to solve the unsteady flows in SJE, and the reasons of thrust fluctuation during the wall-attachment state of SJE are found out. Based on the pressure cloud and streamlines, the vortices generated by the unsteady flow on attached wall had also been investigated and drawn some conclusions.

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Xi, Chao, and Wei Min Sang. "Study of Civil-Plane High-Lift Model Using Omni-Tree Cartesian Grids." Applied Mechanics and Materials 249-250 (December 2012): 1019–24. http://dx.doi.org/10.4028/www.scientific.net/amm.249-250.1019.

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We developed a CFD code applies the omni-tree Cartesian grid to simulate the flow fields around one civil-plane high-lift model using the multi-zone technique. With a face-to-face algorithm, the flow control equations are solved numerically, in combination with the cell-center finite volume method and dual-time stepping scheme. The computed results are in good agreement with the experimental data and show preliminarily that numerical method is effective.

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Kumar, K. Siva, and Sharanappa V. Sajjan. "Unsteady Flow past a Combined Pitching and Plunging Aerofoil Using an Implicit RANS Solver." Applied Mechanics and Materials 110-116 (October 2011): 3481–88. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.3481.

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Unsteady Reynolds-averaged Navier-Stokes (RANS) computations are presented for low Mach number flow past a combined pitching and plunging NACA 0012 aerofoil. The Implicit RANS solver used for obtaining time-accurate solutions is based on a finite volume nodal point spatial discretization scheme with dual time stepping. The aim is to validate the unsteady solver for flapping motion of the aerofoil. Results are presented in the form of aerodynamic coefficients and compared with available literature, thus demonstrating the capability of the solver to provide useful unsteady input data for aeroelastic and aeroacoustic analysis.

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von Hoyningen-Huene, Martin, and Alexander R. Jung. "Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations." Journal of Turbomachinery 122, no. 2 (February 1, 1999): 234–46. http://dx.doi.org/10.1115/1.555440.

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This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a nonaccelerated, fully explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain, and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier–Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The purpose of the comparison of the different numerical algorithms for explicit schemes is to facilitate the decision as to which acceleration technique should be used for calculations with regard to accuracy and computational time. The convergence acceleration methods under consideration are explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid, and implicit dual time stepping. The investigation and comparison of the different acceleration techniques apply to all explicit unsteady flow solvers. This paper also examines the influence of the stage blade count ratio on the flowfield. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is crucial from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages. [S0889-504X(00)00702-9]

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