Building Blocks for Reliable Complex Nonlinear Numerical Simulations

Abstract

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...

Physical and numerical aspects of the high-speed unsteady flow around concave axisymmetric bodies

“…Thus, there is strong interest in understanding the physics of these flows. Furthermore, researchers, for example Yee [5], have published many works on spurious bifurcations of numerical solutions and their connection to initial data, grid fineness and time steps. In the framework of RTO/AVT-136 Task Group, a research has been performed, which included both, the physical and the numerical aspects of the problem.…”

Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

“…This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for nonreacting flows. In addition to the minimization of numerical dissipation while maintaining numerical stability in compressible turbulence with strong shock, Yee & Sjögreen, Yee and Yee & Sweby [32,33,36,37] discussed a general framework for the design of such schemes. Yee & Sjögreen [41], Sjögreen & Yee [27,28,44] and Wang et al [30,31], and references cited therein present their recent progress on the subject.…”

LES of Temporally Evolving Mixing Layers by an Eighth-Order Filter Scheme

“…This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. In addition to the minimization of numerical dissipation while maintaining numerical stability in compressible turbulence with strong shocks, Yee & Sjögreen, Yee and Yee & Sweby [65,66,62,61,68,69] discussed a general framework for the design of such schemes. Yee & Sjögreen [70], Sjögreen & Yee [53] and Wei et al [60] and references cited therein present their recent progress on the subject.…”