Exponential compact higher order scheme and their stability analysis for unsteady convection-diffusion equations

Exponential compact higher-order schemes have been developed for unsteady convection-diffusion equation (CDE). One of the developed scheme is sixth-order accurate which is conditionally stable for the Peclet number 0 <= Pe <= 2.8 and the other is fourth-order accurate which is unconditionally stable. Schemes for two-dimensional (2D) problems are made to use alternate direction implicit (ADI) algorithm. Example problems are solved and the numerical solutions are compared with the analytical solutions for each case.

[1]  D. N. De G. Allen,et al.  RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER , 1955 .

[2]  Alain Rigal.  High order difference schemes for unsteady one-dimensional diffusion-convection problems , 1994 .

[3]  Y. Sanyasiraju,et al.  Spectral resolutioned exponential compact higher order scheme (SRECHOS) for convection–diffusion equations , 2008 .

[4]  A. B. Shamardan,et al.  The numerical treatment of nonlinear parabolic partial differential equations governing convection-diffusion processes , 1988 .

[5]  Jun Zhang,et al.  High order ADI method for solving unsteady convection-diffusion problems , 2004 .

[6]  Y. Ge,et al.  A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems , 2007 .

[7]  B. J. Noye.  A compact unconditionally stable finite‐difference method for transient one‐dimensional advection‐diffusion , 1991 .

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

[9]  M. Ciment,et al.  Review. The Operator Compact Implicit Method for Parabolic Equations , 1978 .

[10]  B. J. Noye,et al.  Finite difference methods for solving the two‐dimensional advection–diffusion equation , 1989 .

[11]  Murli M. Gupta,et al.  A single cell high order scheme for the convection‐diffusion equation with variable coefficients , 1984 .

[12]  Jiten C. Kalita,et al.  A class of higher order compact schemes for the unsteady two‐dimensional convection–diffusion equation with variable convection coefficients , 2002 .

[13]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[14]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations, Second Edition , 2004 .

[15]  Richard S. Varga,et al.  Application of Oscillation Matrices to Diffusion-Convection Equations , 1966 .

[16]  Y. V. S. S. Sanyasiraju,et al.  Characteristic Analysis of Exponential Compact Higher Order Schemes for Convection-Diffusion Equations , 2011, Am. J. Comput. Math..

[17]  Maria Antonietta Pirozzi,et al.  High order finite difference numerical methods for time-dependent convection-dominated problems , 2005 .

[18]  W. Spotz.  Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible streamfunction vorticity , 1998 .

[19]  Donghyun You.  A high-order Padé ADI method for unsteady convection-diffusion equations , 2006, J. Comput. Phys..