Analysis of stability and accuracy of finite-difference schemes on a skewed mesh

Numerical stability and accuracy of finite-difference schemes on a skewed non-uniform mesh are investigated to provide guidelines for mesh design and for devising appropriate solution methods when mesh skewness is unavoidable. In the current analysis, a linear advection-diffusion equation in a Cartesian coordinate system is transformed into a curvilinear one corresponding to a skewed mesh. A finite-difference approximation of the transformed equation leads to the leading-order error terms which are responsible for time-step restrictions and numerical instability. A truncation error analysis of central-difference approximation reveals the effects of mesh non-uniformity and skewness on the solution quality. In addition, a modified wavenumber analysis is performed for the central- and upwind-difference schemes coupled with time-integration methods, to examine the effects of mesh skewness angle and flow direction relative to the mesh angle on the numerical stability. In general, severe mesh skewness leads to restrictions on the allowable cell Peclet number and time-step size and also increases phase and amplitude errors.

[1]  P. Moin,et al.  Computation of Trailing-Edge Flow and Noise Using Large-Eddy Simulation , 2000 .

[2]  Y. M. Tsuei,et al.  A formula for estimation of truncation errors of convection terms in a curvilinear coordinate system , 1992 .

[3]  Parviz Moin,et al.  Large-eddy simulation of a rotor tip-clearance flow , 2001 .

[4]  Arthur Veldman,et al.  Direct Numerical Simulation of Turbulence at Lower Costs , 1997 .

[5]  Robert L. Lee,et al.  Don''t suppress the wiggles|they''re telling you something! Computers and Fluids , 1981 .

[6]  P. Moin.  Fundamentals of Engineering Numerical Analysis , 2001 .

[7]  Theodore H. Okiishi,et al.  Stator-Rotor Interactions in a Transonic Compressor—Part 2: Description of a Loss-Producing Mechanism , 2003 .

[8]  Torsten Fransson,et al.  Viscous and Inviscid Linear/Nonlinear Calculations Versus Quasi-Three-Dimensional Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration , 1999 .

[9]  C. Hah,et al.  A Numerical Modeling of Endwall and Tip-Clearance Flow of an Isolated Compressor Rotor , 1985 .

[10]  C. Fletcher.  Computational techniques for fluid dynamics , 1992 .

[11]  P. Durbin,et al.  Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage , 2001, Journal of Fluid Mechanics.

[12]  Clive A. J. Fletcher,et al.  Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques , 1996 .

[13]  Oleg V. Vasilyev,et al.  High Order Finite Difference Schemes on Non-uniform Meshes with Good Conservation Properties , 2000 .

[14]  A. Veldman,et al.  Spectro-Consistent Discretization of Navier-Stokes: a Challenge to RANS and LES , 1998 .

[15]  Arthur Veldman,et al.  Spectro-Consistent Discretization of Navier-Stokes: a Challenge to RANS and LES , 1998 .

[16]  Vincenzo Armenio,et al.  A Lagrangian Mixed Subgrid-Scale Model in Generalized Coordinates , 2000 .

[17]  Rajat Mittal,et al.  Large-eddy simulation of flow through a low-pressure turbine cascade , 2001 .

[18]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[19]  A. Cain,et al.  Numerical wave propagation analysis for stretched grids , 1994 .

[20]  Malcolm L. Spaulding,et al.  A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems , 2003 .