A Numerical Resolution Study of High Order Essentially Non-Oscillatory Schemes Applied to Incompressible Flow
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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High-order essentially non-oscillatory ENO schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through Fast Fourier Transforms FFT and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large-scale features of the flow when a coarse grid is used and small-scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.
- Numerical Mathematics
- Fluid Mechanics