An implicit fourth order difference method for viscous flows

Authors:
Daniel S. Watanabe and J. Richard Flood

Journal:
Math. Comp. **28** (1974), 27-32

MSC:
Primary 65N05

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341892-7

MathSciNet review:
0341892

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A new implicit finite-difference scheme for viscous flows is presented. The scheme is based on Simpson's rule and two-point Hermite interpolation, is uniformly accurate to fourth order in time and space, and is unconditionally stable according to a Fourier stability analysis. Numerical solutions of Burger's equation are presented to illustrate the order and accuracy of the scheme.

**[1]**C. G. Broyden, "A new method of solving nonlinear simultaneous equations,"*Comput. J.*, v. 12, 1969/70, pp. 94-99. MR**39**#6509. MR**0245197 (39:6509)****[2]**S. Z. Burstein & A. A. Mirin, "Third order difference methods for hyperbolic equations,"*J. Computational Phys.*, v. 5, 1970, pp. 547-571. MR**43**#8255. MR**0282545 (43:8255)****[3]**R. W. MacCormack, "Numerical solution of the interaction of a shock wave with a laminar boundary layer,"*Lecture Notes in Physics*, v. 8, Springer-Verlag, Berlin, 1971, pp. 151-163.**[4]**E. L. Rubin & S. Z. Burstein, "Difference methods for the inviscid and viscous equations of a compressible gas,"*J. Computational Phys.*, v. 2, 1967, pp. 178-196.**[5]**V. V. Rusanov, "On difference schemes of third order accuracy for nonlinear hyperbolic systems,"*J. Computational Phys.*, v. 5, 1970, pp. 507-516. MR**43**#1452. MR**0275699 (43:1452)****[6]**G. Zwas & S. Abarbanel, "Third and fourth order accurate schemes for hyperbolic equations of conservation law form,"*Math. Comp.*, v. 25, 1971, pp. 229-236. MR**0303766 (46:2902)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65N05

Retrieve articles in all journals with MSC: 65N05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341892-7

Keywords:
Partial differential equations,
initial-value problems,
finite-difference schemes,
unconditional stability,
high order accuracy,
viscous flows

Article copyright:
© Copyright 1974
American Mathematical Society