Linear Schemes - structured grids
From CFD-Wiki
(→Fromm - Fromm's Upwind Scheme) |
|||
(5 intermediate revisions not shown) | |||
Line 1: | Line 1: | ||
- | == | + | == Introduction == |
- | + | Linear schemes UDS, CDS and these | |
+ | |||
+ | == SOU - Second Order Upwind (also LUDS or UDS-2) == | ||
{{reference-paper | author=S.P.Vanka | title=Second-order upwind differencing ina recirculating flow | rest=AIAA J., 25, 1435-1441}} | {{reference-paper | author=S.P.Vanka | title=Second-order upwind differencing ina recirculating flow | rest=AIAA J., 25, 1435-1441}} | ||
Line 7: | Line 9: | ||
{{reference-paper | author=R.F.Warming and R.M. Beam | year= 1976 | title= Upwind second order difference schemes and applications in aerodynamics flows | rest= AIAA J. 14 (1976) 1241-1249 }} | {{reference-paper | author=R.F.Warming and R.M. Beam | year= 1976 | title= Upwind second order difference schemes and applications in aerodynamics flows | rest= AIAA J. 14 (1976) 1241-1249 }} | ||
- | + | == Skew - Upwind == | |
'''G.D.Raithby ''', Skew upstream differencing schemes for problems involving fluid flow, Computational Methods Applied Mech. Engineering, 9, 153-164 (1976) | '''G.D.Raithby ''', Skew upstream differencing schemes for problems involving fluid flow, Computational Methods Applied Mech. Engineering, 9, 153-164 (1976) | ||
- | + | == QUICK - Quadratic Upwind Interpolation for Convective Kinematics (also UDS-3 or QUDS) == | |
'''B.P.Leonard''', A stable and accurate modelling procedure based on quadratic interpolation, Comput. Methods Appl. Mech. Engrg. 19 (1979) 58-98 | '''B.P.Leonard''', A stable and accurate modelling procedure based on quadratic interpolation, Comput. Methods Appl. Mech. Engrg. 19 (1979) 58-98 | ||
Line 17: | Line 19: | ||
Usual variables | Usual variables | ||
- | |||
- | |||
- | |||
- | |||
- | |||
Line 48: | Line 45: | ||
Normalised variables (non-uniform grid) | Normalised variables (non-uniform grid) | ||
- | |||
- | |||
- | |||
- | |||
- | |||
- | |||
- | |||
- | |||
- | |||
- | |||
<table width="100%"><tr><td> | <table width="100%"><tr><td> | ||
Line 77: | Line 64: | ||
</td><td width="5%">(2)</td></tr></table> | </td><td width="5%">(2)</td></tr></table> | ||
- | + | == LUS - Linear Upwind Scheme == | |
- | + | {{reference-paper | author=H.C.Price, R.S. Varga and J.E.Warren | year= 1966 | title= Application of oscillation matrices to diffusion-convection equations | rest= Journal Math. and Phys., Vol. 45, p.301, (1966) }} | |
- | + | ||
- | + | ||
+ | <table width="100%"><tr><td> | ||
+ | :<math> | ||
+ | \phi_{f}= \phi_{C} + 0.5 \left( \phi_{C} - \phi_{U} \right) | ||
+ | </math> | ||
+ | </td><td width="5%">(1)</td></tr></table> | ||
- | + | == Fromm - Fromm's Upwind Scheme == | |
- | + | == CUDS - Cubic Upwind Difference Scheme (also CUS or UDS-4) == | |
In CUDS (UDS-4) for interpolation of function is used three upwind nodes and one node downstream. | In CUDS (UDS-4) for interpolation of function is used three upwind nodes and one node downstream. | ||
Line 94: | Line 84: | ||
<table width="100%"><tr><td> | <table width="100%"><tr><td> | ||
:<math> | :<math> | ||
- | + | \phi_{w}=\frac{1}{3}\phi_{P} + \frac{5}{6}\phi_{W} + \frac{1}{6}\phi_{WW} | |
</math> | </math> | ||
</td><td width="5%">(2)</td></tr></table> | </td><td width="5%">(2)</td></tr></table> | ||
Line 102: | Line 92: | ||
<table width="100%"><tr><td> | <table width="100%"><tr><td> | ||
:<math> | :<math> | ||
- | \hat{ | + | \hat{\phi_{w}}=\frac{1}{3} + \frac{5}{6}\hat{\phi_{W}} |
</math> | </math> | ||
</td><td width="5%">(2)</td></tr></table> | </td><td width="5%">(2)</td></tr></table> | ||
Line 112: | Line 102: | ||
Paper No. AIAA-81-0112, AIAA 19th Aerospace Science Meeting, St. Louis, 1982. | Paper No. AIAA-81-0112, AIAA 19th Aerospace Science Meeting, St. Louis, 1982. | ||
- | + | == CUI - Cubic Upwind Interpolation == | |
B.P. Leonard | B.P. Leonard |
Latest revision as of 01:11, 9 November 2005
Introduction
Linear schemes UDS, CDS and these
SOU - Second Order Upwind (also LUDS or UDS-2)
S.P.Vanka ({{{year}}}), "Second-order upwind differencing ina recirculating flow", AIAA J., 25, 1435-1441.
R.F.Warming and R.M. Beam (1976), "Upwind second order difference schemes and applications in aerodynamics flows", AIAA J. 14 (1976) 1241-1249.
Skew - Upwind
G.D.Raithby , Skew upstream differencing schemes for problems involving fluid flow, Computational Methods Applied Mech. Engineering, 9, 153-164 (1976)
QUICK - Quadratic Upwind Interpolation for Convective Kinematics (also UDS-3 or QUDS)
B.P.Leonard, A stable and accurate modelling procedure based on quadratic interpolation, Comput. Methods Appl. Mech. Engrg. 19 (1979) 58-98
Usual variables
| (2) |
| (2) |
Normalised variables (uniform grid)
| (2) |
Normalised variables (non-uniform grid)
| (2) |
| (2) |
LUS - Linear Upwind Scheme
H.C.Price, R.S. Varga and J.E.Warren (1966), "Application of oscillation matrices to diffusion-convection equations", Journal Math. and Phys., Vol. 45, p.301, (1966).
| (1) |
Fromm - Fromm's Upwind Scheme
CUDS - Cubic Upwind Difference Scheme (also CUS or UDS-4)
In CUDS (UDS-4) for interpolation of function is used three upwind nodes and one node downstream.
usual variables
| (2) |
normalised variables (uniform grids)
| (2) |
R.K. Aragval
A third-order-accurate upwind scheme for Navier-Stokes solution at high Reynolds numbers
Paper No. AIAA-81-0112, AIAA 19th Aerospace Science Meeting, St. Louis, 1982.
CUI - Cubic Upwind Interpolation
B.P. Leonard
A survey of finite differences of opinion on numerical muddling of incompressible defective confusion equation
paper in ASME, Applied Mechanics Division, Winter Annual Meeting, 1979
Return to Numerical Methods
Return to Approximation Schemes for convective term - structured grids