Under-Resolution and Diagnostics in Spectral Simulations of Complex-Geometry Flows
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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Large-scale simulations are often under-resolved at some level, but they are still useful in extracting both qualitative and quantitative information about the flow. In order to use such results effectively we need to characterize the numerical uncertainty of under-resolved simulations. However, different numerical methods exhibit different, behavior, and spectral-based methods in particular may over-predict fluctuations both in amplitude and frequency due to their very low artificial dissipation in contrast with finite differences. In this chapter, we provide insight into under-resolved spectral simulations and document several diagnostic signs of under-resolution for spectralhp element methods. We first review the state-of-the-art in direct numerical simulation and present a new class of spectral methods on unstructured grids for handling complex-geometry compressible and incompressible flows. We the focus on the effects of under-resolving the nonlinear contributions, and finally we present prototype cases for both transitional and turbulent flows.
- Numerical Mathematics
- Operations Research
- Fluid Mechanics