A critical evaluation of the resolution properties of B-Spline and compact finite difference methods

Resolution properties of B-spline and compact finite difference schemes are compared using Fourier analysis in periodic domains, and tests based on solution of the wave and heat equations in finite domains, with uniform and nonuniform grids. Results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution. However, B-spline schemes have a more straightforward and robust formulation, particularly near boundaries on nonuniform meshes.

[1]  K. Viswanadham,et al.  Finite element method for one-dimensional and two-dimensional time dependent problems with B-splines , 1993 .

[2]  R. Moser,et al.  Two-Dimensional Mesh Embedding for B-spline Methods , 1998 .

[3]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[4]  A. Patera.  A spectral element method for fluid dynamics: Laminar flow in a channel expansion , 1984 .

[5]  D. J. Fyfe,et al.  The use of cubic splines in the solution of two-point boundary value problems , 1969, Comput. J..

[6]  On finite element analysis of compressible and incompressible, temperature-dependent fluid flow , 1981 .

[7]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[8]  M Israeli,et al.  Numerical Simulation of Viscous Incompressible Flows , 1974 .

[9]  George Em Karniadakis,et al.  Spectral element simulations of laminar and turbulent flows in complex geometries , 1989 .

[10]  P. Khosla,et al.  Polynomial interpolation methods for viscous flow calculations , 1977 .

[11]  Krishnan Mahesh,et al.  High order finite difference schemes with good spectral resolution , 1997 .

[12]  Jonathan B. Freund,et al.  Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate , 1997, Journal of Fluid Mechanics.

[13]  J. Oden,et al.  The h-p adaptive finite element method for the numerical simulation of compressible flow , 1988 .

[14]  Parviz Moin,et al.  Zonal Embedded Grids for Numerical Simulations of Wall-Bounded Turbulent Flows , 1996 .

[15]  R. Hirsh,et al.  Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique , 1975 .

[16]  S. G. Rubin,et al.  Higher-Order Numerical Solutions Using Cubic Splines , 1976 .

[17]  Burton Wendroff,et al.  The Relation Between the Galerkin and Collocation Methods Using Smooth Splines , 1974 .

[18]  R. A. Graves,et al.  Viscous flow solutions with a cubic spline approximation , 1975 .

[19]  Steven A. Orszag.  On the Resolution Requirements of Finite-Difference Schemes , 1971 .

[20]  D. Gottlieb,et al.  The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes , 1993 .

[21]  A. M. Davies.  Application of the galerkin method to the solution of burgers' equation , 1978 .

[22]  B. Gustafsson.  The convergence rate for difference approximations to mixed initial boundary value problems , 1975 .

[23]  A. M. Davies,et al.  The use of the galerkin method with a basis of B-Splines for the solution of the one-dimensional primitive equations , 1978 .

[24]  Marcelo H. Kobayashi,et al.  Regular Article: On a Class of Padé Finite Volume Methods , 1999 .

[25]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[26]  P. Spalart.  Direct simulation of a turbulent boundary layer up to Rθ = 1410 , 1988, Journal of Fluid Mechanics.

[27]  Steven A. Orszag,et al.  Numerical simulation of incompressible flows within simple boundaries: accuracy , 1971, Journal of Fluid Mechanics.

[28]  S. Lele,et al.  Vortex-induced disturbance field in a compressible shear layer , 1993 .

[29]  P. Moin,et al.  Numerical Simulation of Turbulent Flows , 1984 .