An interpolation based finite difference method on non-uniform grid for solving Navier stokes equations
Chen, Jim C.
Lo, Edmond Yat-Man
Date of Issue2014
School of Civil and Environmental Engineering
This paper presents a Hermite polynomial interpolation based method to construct high-order accuracy finite difference schemes on non-uniform grid. This method can achieve arbitrary order accuracy by expanding the grid stencil and involving higher order derivatives. The paper first constructs combined compact difference schemes, from which compact difference schemes and super-compact difference schemes are shown to be derived by linear operations. Explicit schemes are further shown to be particular cases of this interpolation method. Using the present derivation method, previously reported classical schemes can be constructed on non-uniform grid and a new 5-point combined compact difference scheme is developed in particular. A new 2-piecewise function is also provided for non-uniform grid generation. The first piece of function stabilizes the scheme on Dirichlet boundary by clustering the grid points appropriately and the second piece is to stretch the outer grids according to the simulation domain of interest. This new scheme with non-uniform grid shows excellent stability properties and high spectral resolution as compared with other classical compact and combined compact difference schemes. To further demonstrate the present scheme, simulation of boundary layer transition problems using the three-dimensional incompressible Navier–Stokes equations is performed and good agreement with experimental results is obtained.
DRNTU::Engineering::Civil engineering::Water resources
Computers & fluids
© 2014 Elsevier Ltd. This is the author created version of a work that has been peer reviewed and accepted for publication by Computers & Fluids, Elsevier Ltd. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI:http://dx.doi.org/10.1016/j.compfluid.2014.05.008].