A study of finite difference approximations to steady-state, convection-dominated flow problems

Abstract Five different finite difference schemes, first-order upwind, skew upwind, second-order upwind, second order central differencing, and QUICK, approximating the convection terms in the transport equation with fluid motion, have been studied. Three simple test problems are used to compare the performances by the five schemes for high cell Peclet number flows; they are also used to demonstrate the restraints on the accuracy of the numerical approximations set by the types of the boundary conditions, by the presence of the source term in the flow region, and by the skewness of the numerical grid lines. The basic reasons behind the spurious oscillations in a numerical solution are studied. Among all five schemes studied, the second-order upwind is found to be, in general, the most satisfactory.

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

[2]  I. Castro.  Numerical Difficulties in the Calculation of Complex Turbulent Flows , 1979 .

[3]  Åke Björck,et al.  Numerical Methods , 2021, Markov Renewal and Piecewise Deterministic Processes.

[4]  C. Dalton,et al.  Numerical study of viscous flow in a cavity , 1973 .

[5]  C. K. Chu,et al.  Numerical Methods in Fluid Dynamics , 1979 .

[6]  Wolfgang Rodi,et al.  Calculation of Annular and Twin Parallel Jets Using Various Discretization Schemes and Turbulence-Model Variations , 1981 .

[7]  G. R. Shubin,et al.  Computational accuracy and mesh reynolds number , 1978 .

[8]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[9]  A. B. Strong,et al.  PROPOSAL FOR A NEW DISCRETE METHOD BASED ON AN ASSESSMENT OF DISCRETIZATION ERRORS , 1980 .

[10]  G. D. Raithby,et al.  Skew upstream differencing schemes for problems involving fluid flow , 1976 .

[11]  G. D. Raithby,et al.  A critical evaluation of upstream differencing applied to problems involving fluid flow , 1976 .

[12]  O. Burggraf.  Analytical and numerical studies of the structure of steady separated flows , 1966, Journal of Fluid Mechanics.

[13]  R. Maccormack,et al.  Numerical Solution of Compressible Viscous Flows , 1979 .

[14]  Wei Shyy,et al.  Determination of relaxation factors for high cell peclet number flow simulation , 1984 .

[15]  G. de Vahl Davis,et al.  An evaluation of upwind and central difference approximations by a study of recirculating flow , 1976 .

[16]  F. G. Blottner,et al.  Influence of boundary approximations and conditions on finite-difference solutions , 1982 .

[17]  M. Israeli,et al.  Efficiency of Navier-Stokes Solvers , 1977 .

[18]  A critique of a second-order upwind scheme for viscous flow problems , 1978 .

[19]  B. Launder,et al.  A comparison of hybrid and quadratic-upstream differencing in high Reynolds number elliptic flows , 1981 .

[20]  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 .

[21]  Michael A. Leschziner,et al.  Practical evaluation of three finite difference schemes for the computation of steady-state recirculating flows , 1980 .

[22]  L. C. Woods,et al.  Field Computations in Engineering and Physics , 1962 .

[23]  A. D. Gosman,et al.  Heat and Mass Transfer in Recirculating Flows , 1969 .