Simulation of transitional flows
The purpose of this work is to validate Navier–Stokes (NS) solvers implemented in FEniCS for 12416 unstable, transitional flows. Solvers for the NS equations have been discussed in Chapter 21 for 12417 laminar flows. In this chapter, focus is put more directly on energy and energy conservation, features 12418 of primary importance in turbulence applications. We emphasize the treatment of the nonlinear 12419 convection term, where various forms (standard, divergence and skew-symmetric) are implemented 12420 and tested for both accuracy and stability. The algorithm chosen to advance the momentum and 12421 pressure in time is a fractional step approach that is memory efficient, but incurs a splitting error due 12422 to the uncoupling of the velocity and pressure. The significance of this splitting error is validated 12423 through comparison with a more accurate fully coupled solver that, due to its higher memory cost, 12424 is less suitable for large-scale turbulence applications. The performance of the solvers is validated 12425 with the one-dimensional Burgers’ equation, the Orr–Sommerfeld perturbation in two dimensions 12426 and finally the three-dimensional unstable and transitional Taylor–Green vortex.
KeywordsLarge Eddy Simulation Direct Numerical Simulation Fractional Step Fractional Step Method Chebyshev Point
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