Balancing aspects of numerical dissipation, dispersion, and aliasing in time‐accurate simulations

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SummaryThe current study looks at the selection of scheme elements that are well‐suited for long‐time integration of unsteady flows in the absence or under‐resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best‐case scenario for overall spectral resolvability. High‐order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew‐symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale‐discriminant artificial‐dissipation methods are incorporated for de‐aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor‐Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.