A Semi-Lagrangian High-Order Methodfor Navier–Stokes Equations
نویسندگان
چکیده
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(1t k + 1x p+1 1t ). 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. Twoand 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. c © 2001 Academic Press
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