Abstract
Accurate reference solutions are very important in stability analysis, where they must act as a reliable base-state. They are also quite useful for unsteady numerical simulations, where they play key roles as initial conditions and in the implementation of boundary conditions, such as buffer zones. Quite often they are approximate solutions for a simplified version of the particular problem at hand, such as boundary-layer solutions. However, these approximate solutions are usually not available, their development is problem dependent and they may not be accurate enough. Hence, there is a need for methodologies that are capable of generating steady-states for arbitrary unsteady differential models. One attempt in this direction is the selective frequency damping technique, despite being developed for problems with a well defined self-excitation frequency. Another attempt to do so is the physical-time damping technique, but temporal dissipation is proportional to the time step. Since numerical instability can keep this time step too small in many nonlinear problems, this technique may not be able to introduce enough dissipation for the damping of all perturbations in very unstable flows. The present work overcomes this problem by noting that optimal damping is not introduced through maximum temporal dissipation, but minimal gain. The implicit Euler scheme employed in the physical-time damping technique achieves both in the limit of infinite CFL numbers, which usually cannot be imposed due to nonlinear effects. This time marching scheme was modified in order for its minimal gain to occur at smaller CFL numbers. Several test cases confirm the efficacy of this new approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Michalke A (1984) Prog Aerosp Sci 21:159
Steinberg S, Roache PJ (1985) J Comput Phys 57:251
Roache PJ (2002) J Fluids Eng 124:4
Jones LE, Sandberg RD, Sandham ND (2010) J Fluid Mech 648:257
Theofilis V (2003) Prog Aerosp Sci 39:249
Alves LSdeB, Kelly RE, Karagozian AR (2008) J Fluid Mech 602:383.
Kelly RE, Alves LSdeB (2008) Philos Trans R Soc Lond Ser A: Math Phys Sci 366:2729.
Bagheri S, Schlatter P, Schmid PJ, Henningson DS (2009) J Fluid Mech 624:33
Theofilis V (2011) Annu Rev Fluid Mech 43:319
Lardjane N, Fedioun I, Gokalp I (2004) Comput Fluids 33:549
Germanos RAC, de Souza LF, de Medeiros MAF (2009) J Braz Soc Mech Sci Eng 31(2):125
Bijl H, Carpenter MH, Vatsa VN, Kennedy CA (2002) J Comput Phy 179:313
Wang L, Mavriplis DJ (2007) J Comput Phys 225(2):1994
Blaschak JG, Kriegsmann GA (1988) J Comput Phys 77:109
Bodony DJ (2006) J Comput Phys 212(2):681
Colonius T, Lele SK (2004) Prog Aerosp Sci 40:345
Saric WS, Reed HL, White EB (2003) Annu Rev Fluid Dyn 35:413
Collis SS, Lele SK (1999) J Fluid Mech 380:141
Barone MF, Lele SK (2002) In: AIAA conference paper 0226, pp 1–12.
Barone MF, Lele SK (2005) J Fluid Mech 540:301
Tuckerman LS, Barkley D (2000) Bifurcation analysis for time steppers. In: Numerical methods for bifurcation problems and large-scale dynamical systems (The IMA volumes in mathematics and its applications, 2000), vol 119, pp 453–466.
Åkervik E, Brandt L, Henningson DS, Hoepffner J, Marxen O, Schlatter P (2006) Phys Fluids 18(6):068102
RdeS Teixeira, Alves LSdeB, (2012) Int J Comput. Fluid Dyn 26:67
Tannehill JC, Anderson DA, Pletcher RH (1997) Computational fluid mechanics and heat transfer. Taylor & Francis, Philadelphia
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Teixeira, R.d.S., Alves, L.S.d.B. (2015). Minimal Gain Time Marching Schemes for the Construction of Accurate Steady-States. In: Theofilis, V., Soria, J. (eds) Instability and Control of Massively Separated Flows. Fluid Mechanics and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-06260-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-319-06260-0_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06259-4
Online ISBN: 978-3-319-06260-0
eBook Packages: EngineeringEngineering (R0)