docs:utils:couette
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| ''couette'' integrates plane Couette or channel flow from a given initial condition and save velocity fields to disk at a regular interval. (It should probably be called ''integrate''; I might change it to that in the next release.) | ''couette'' integrates plane Couette or channel flow from a given initial condition and save velocity fields to disk at a regular interval. (It should probably be called ''integrate''; I might change it to that in the next release.) | ||
| - | |||
| ====== main options ====== | ====== main options ====== | ||
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| -P --dPdx <real> default == 0 value for fixed pressure gradient | -P --dPdx <real> default == 0 value for fixed pressure gradient | ||
| -U --Ubulk <real> default == 0 value for fixed bulk velocity | -U --Ubulk <real> default == 0 value for fixed bulk velocity | ||
| + | -symms --symmetries <string> default == "" filename for generators of flow-invariant symmetry subspace | ||
| <flowfield> (trailing arg 1) initial condition | <flowfield> (trailing arg 1) initial condition | ||
| </code> | </code> | ||
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| [[docs:utils:couette:alloptions|Complete option list]] | [[docs:utils:couette:alloptions|Complete option list]] | ||
| - | ==== time intervals ==== | + | ===== time intervals ===== |
| The integration starts at ''t=T0'' and saves data at times ''t = T0 + n dT'', exactly. The ''dt'' | The integration starts at ''t=T0'' and saves data at times ''t = T0 + n dT'', exactly. The ''dt'' | ||
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| so that the save interval is exactly what you asked for. Data is saved to disk in files named ''u0.ff, u1.ff, u2.ff, ...'' if ''t'' takes on integer values or filenames with four-digit precision if ''t'' otherwise, e.g. ''u0.000.ff, u0.125.ff, u0.250.ff, ...''. The integration stops when ''t = T0 + n dT > T1.'' | so that the save interval is exactly what you asked for. Data is saved to disk in files named ''u0.ff, u1.ff, u2.ff, ...'' if ''t'' takes on integer values or filenames with four-digit precision if ''t'' otherwise, e.g. ''u0.000.ff, u0.125.ff, u0.250.ff, ...''. The integration stops when ''t = T0 + n dT > T1.'' | ||
| - | ==== timestepping ==== | + | ===== timestepping ===== |
| The ''-ts'' or ''--timestepping'' sets the finite-difference time stepping algorithm. It takes the following | The ''-ts'' or ''--timestepping'' sets the finite-difference time stepping algorithm. It takes the following | ||
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| |''sbdf3''| 3 |Semi-implict Backwards Differentiation| | |''sbdf3''| 3 |Semi-implict Backwards Differentiation| | ||
| |''sbdf4''| 4 | Semi-implict Backwards Differentiation| | |''sbdf4''| 4 | Semi-implict Backwards Differentiation| | ||
| + | ===== nonlinearity ===== | ||
| - | ==== nonlinearity ==== | + | The ''-nl'' or ''--nonlinearity'' specifies the method for calculating the |
| + | nonlinearity u⋅∇u in the Navier-Stokes equation. | ||
| - | ====== Usage examples ====== | + | ^ value ^ ^method^ |
| + | |''rot''| (∇×u)×u |rotational| | ||
| + | |''conv''| u⋅∇u |convection| | ||
| + | |''div''| ∇⋅(uu) |divergence| | ||
| + | |''skew''| (u⋅∇u + ∇⋅(uu))/2 |skew-symmetric| | ||
| + | |''alt''| |alternating between ''conv'' and ''div''| | ||
| + | ===== mean constraints ===== | ||
| + | ===== symmetries ===== | ||
| - | Integrate | + | The ''-symms filename.asc'' option will cause the numerically integrated solution to be periodically projected onto a flow-invariant symmetric subspace specified by the named file. The file should list the generators of the subspace's symmetry group. For example, suppose you want to restrict integration to the symmetry group ''S = {s1,s2,s3}'' |
| + | |||
| + | <latex> | ||
| + | $ \begin{align*} | ||
| + | s_1 \, [u, v, w](x,y,z) &= [u, v, -w](x+L_x/2, y, -z) \\ | ||
| + | s_2 \, [u, v, w](x,y,z) &= [-u, -v, w](-x+L_x/2,-y,z+L_z/2) \\ | ||
| + | s_3 \, [u, v, w](x,y,z) &= [-u,-v,-w](-x, -y, -z+L_z/2) \\ | ||
| + | \end{align*} | ||
| + | $ | ||
| + | </latex> | ||
| + | |||
| + | s1 and s2 are generators of S. So construct a file s1s2.asc with these contents | ||
| + | |||
| + | % 2 | ||
| + | 1 1 1 -1 0.5 0.0 | ||
| + | 1 -1 -1 1 0.5 0.5 | ||
| + | |||
| + | The first line specifies the number of generators, and the following lines specify the generators, according to | ||
| + | |||
| + | c sx sy sz ax az | ||
| + | |||
| + | where | ||
| + | |||
| + | (c sx sy sz ax az) [u, v, w](x, y, z) → c [sx u, sy v, sz w](sx x + ax Lx, sy y, sz z + az Lz) | ||
| + | |||
| + | This functionality is provided because numerical errors and instability of invariant symmetric subspaces will cause numerical solutions to drift out of the invariant subspaces. The integration routines do the project at intervals ''dT''. | ||
| + | |||
| + | |||
| + | ====== Usage examples ====== | ||
docs/utils/couette.1234542747.txt.gz · Last modified: 2009/02/13 08:32 by gibson
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