Higher order approximations in fluid mechanisms: Compact to spectral
Abstract
Higher order methods for solving the NavierStokes equations are introduced. Compact methods, Hermitian methods (collocation and difference), Mehrstellen methods, Pade methods and splines are reviewed. Pseudospectral Chebyshev methods are presented. The Chebyshev grid, which clusters interpolation points near the boundaries of a domain, is almost a natural coordinate transformation in the high gradient region, and may allow higher Reynolds numbers to be computed for the same number of modes as finite difference methods. However, there is an upper limit to the Reynolds number which can be reliably calculated for each grid, so coordinate transformations have to be resorted to.
 Publication:

In Von Karman Inst. for Fluid Dynamics Computational Fluid Dyn
 Pub Date:
 1983
 Bibcode:
 1983cofd....1.....H
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 NavierStokes Equation;
 Coordinate Transformations;
 Finite Difference Theory;
 Hermitian Polynomial;
 Interpolation;
 Pade Approximation;
 Spline Functions;
 Fluid Mechanics and Heat Transfer