Abstract
Steady solutions characterized by downstream boundary layers are sought to the one-dimensional linearized Burgers equation for a variety of computational-that is, spatial and temporal differencing-schemes. When well resolved, the presence of these boundary layers does not seriously affect the accuracy of the interior solutions. For narrow outflow boundary layers, however, the Chebyshev collocation method may be unstable, unlike the finite-difference technique, for grid Reynolds numbers less than a certain critical value. Although the spectral solutions are improved by using fractional step time-differencing methods in which the viscous and advective effects are separately treated, the stability of the resulting multistep technique need not be guaranteed by the stability of its component steps. Analogous computational restrictions on the use of the Chebyshev collocation method are shown to hold for the nonlinear Burgers equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 313-324 |
| Number of pages | 12 |
| Journal | Journal of Computational Physics |
| Volume | 33 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 1979 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Physics and Astronomy (miscellaneous)
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Resolution of downstream boundary layers in the Chebyshev approximation to viscous flow problems. / Haidvogel, Dale.
In: Journal of Computational Physics, Vol. 33, No. 3, 01.01.1979, p. 313-324.Research output: Contribution to journal › Article
TY - JOUR
T1 - Resolution of downstream boundary layers in the Chebyshev approximation to viscous flow problems
AU - Haidvogel, Dale
PY - 1979/1/1
Y1 - 1979/1/1
N2 - Steady solutions characterized by downstream boundary layers are sought to the one-dimensional linearized Burgers equation for a variety of computational-that is, spatial and temporal differencing-schemes. When well resolved, the presence of these boundary layers does not seriously affect the accuracy of the interior solutions. For narrow outflow boundary layers, however, the Chebyshev collocation method may be unstable, unlike the finite-difference technique, for grid Reynolds numbers less than a certain critical value. Although the spectral solutions are improved by using fractional step time-differencing methods in which the viscous and advective effects are separately treated, the stability of the resulting multistep technique need not be guaranteed by the stability of its component steps. Analogous computational restrictions on the use of the Chebyshev collocation method are shown to hold for the nonlinear Burgers equation.
AB - Steady solutions characterized by downstream boundary layers are sought to the one-dimensional linearized Burgers equation for a variety of computational-that is, spatial and temporal differencing-schemes. When well resolved, the presence of these boundary layers does not seriously affect the accuracy of the interior solutions. For narrow outflow boundary layers, however, the Chebyshev collocation method may be unstable, unlike the finite-difference technique, for grid Reynolds numbers less than a certain critical value. Although the spectral solutions are improved by using fractional step time-differencing methods in which the viscous and advective effects are separately treated, the stability of the resulting multistep technique need not be guaranteed by the stability of its component steps. Analogous computational restrictions on the use of the Chebyshev collocation method are shown to hold for the nonlinear Burgers equation.
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U2 - https://doi.org/10.1016/0021-9991(79)90158-X
DO - https://doi.org/10.1016/0021-9991(79)90158-X
M3 - Article
VL - 33
SP - 313
EP - 324
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 3
ER -