DYNAMICAL APPROACH STUDY OF SPURIOUS STEADY-STATE NUMERICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS II.<i>GLOBAL ASYMPTOTIC BEHAVIOR OF TIME DISCRETIZATIONS</i>

Yee, H. C.; Sweby, P. K.

doi:10.1080/10618569508904525

Cited by 23 publications

(27 citation statements)

References 19 publications

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“…The importance of the spurious-eddies issue extends beyond elusive intellectual challenge of the numerical analysis itself. The phenomena of stable and unstable multiple solutions and of spurious steady states, which can occur below and above the linearized stability limit of a numerical method, attract increasing interests in the literature [see (44) and the references therein]. Here, we demonstrated the significance of the nonlinear dynamical behavior of the numerical scheme used for discretizing the advective term of the Navier-Stokes equations.…”

Section: Discussionmentioning

confidence: 95%

On Spurious Vortical Structures

Drikakis¹,

Smolarkiewicz

2001

Journal of Computational Physics

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Section: Discussionmentioning

confidence: 95%

On Spurious Vortical Structures

Drikakis¹,

Smolarkiewicz

2001

Journal of Computational Physics

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“…Occurrence of stable and unstable spurious steady states below the linearized stability limit of the scheme (for constant time steps) [1 -4]. Stabilization of unstable steady states by implicit and semi-implicit methods [2][3][4]. Interplay of initial data and time steps on the occurrence of spurious asymptotes [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

On spurious behavior of CFD simulations

Yee

Torczynski

Morton

et al. 1999

Int. J. Numer. Meth. Fluids

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Spurious behavior in underresolved grids and/or semi-implicit temporal discretizations for four computational fluid dynamics (CFD) simulations are studied. The numerical simulations consist of (a) a 1-D chemically relaxed nonequilibrium model, (b) the direct numerical simulation (DNS) of 2-D incompressible flow over a backward facing step, (c) a loosely-coupled approach for a 2-D fluid-structure interaction, and (d) a 3-D compressible unsteady flow simulation of vortex breakdown in delta wings. Using knowledge from dynamical systems theory, various types of spurious behaviors that are numerical artifacts were systematically identified. These studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by the available computing power. In large scale computations underresolved grids, semi-implicit procedures, loosely-coupled implicit procedures, and insufficiently long time integration in DNS are most often unavoidable. Consequently, care must be taken in both computation and in interpretation of the numerical data. The results presented confirm the important role that dynamical systems theory can play in the understanding of the nonlinear behavior of numerical algorithms and in aiding the identification of the sources of numerical uncertainties in CFD.

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“…See Yee & Sweby (1992, 1997) for a discussion. Consequently, a possible numerically induced chaotic transient is especially worrisome in direct numerical simulations of the transition from laminar to turbulent flows.…”

Section: 3mentioning

confidence: 99%

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

Yee

2004

Turbulent Flow Computation

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This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings.The situation is complicated by the fact that the avail- IntroductionThe last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air https://ntrs.nasa.gov/search.jsp?R=20020050374 2018-05-11T14:29:44+00:00Z !, _k and space transportation systems, and systems for planetary and atmospheric sciences, and astrobiology research. In particular, it plays a major role in the success of the US Accelerated Strategic Computing Initiative (ASCI) and its five Academic Strategic Alliance Program (ASAP) centers. Stochasticity stands alongside nonlinearity and the presence of multiscale physical processes as a predominant feature of the scope of this research. The need to guarantee PAR becomes acute when computations offer the ONLY way of generating this type of data limited simulations, the experimental means being unfeasible for any of a number of possible reasons. Examples of this type of data limited problem are:• Stability behavior of re-entry vehicles at high speeds and flow conditions beyond the operating ranges of existing wind tunnelsFlow field in thermo-chemical nonequilibrium around space vehicles traveling at hypersonic velocities through the atmosphere (lack sufficient experimental or analytic validation) Aerodynamics of aircraft in time-dependent maneuvers at high angles of attack (free of interference from support structures, wind-tunnel walls etc., and able to treat flight at extreme and unsafe operating conditions) Stability issues of unsteady separated flows in the absence of all the unwanted disturbances typical of wind-tunnel experiments (e.g., geometrically imperfect free-stream turbulence)This chapter describes some of the building blocks to ensure a higher level of confidence in the PAR of numerical simulation of the aforementioned multi scale complex nonlinear problems, especially the related turbulence flow computations. To isolate the source of numerical uncertainties, the possible discrepancy between the chosen model and the real physics and/or experim...

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DYNAMICAL APPROACH STUDY OF SPURIOUS STEADY-STATE NUMERICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS II.GLOBAL ASYMPTOTIC BEHAVIOR OF TIME DISCRETIZATIONS

Cited by 23 publications

References 19 publications

On Spurious Vortical Structures

On Spurious Vortical Structures

On spurious behavior of CFD simulations

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

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