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A Semi-Lagrangian High-Order Method for Navier–Stokes Equations

✍ Scribed by Dongbin Xiu; George Em Karniadakis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
323 KB
Volume
172
Category
Article
ISSN
0021-9991

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✦ Synopsis

We present a semi-Lagrangian method for advection-diffusion and incompressible Navier-Stokes equations. The focus is on constructing stable schemes of secondorder temporal accuracy, as this is a crucial element for the successful application of semi-Lagrangian methods to turbulence simulations. We implement the method in the context of unstructured spectral/hp element discretization, which allows for efficient search-interpolation procedures as well as for illumination of the nonmonotonic behavior of the temporal (advection) error of the form: O( t k + x p+1 t ). We present numerical results that validate this error estimate for the advection-diffusion equation, and we document that such estimate is also valid for the Navier-Stokes equations at moderate or high Reynolds number. Two-and three-dimensional laminar and transitional flow simulations suggest that semi-Lagrangian schemes are more efficient than their Eulerian counterparts for high-order discretizations on nonuniform grids.

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