ex_tube: Water Tube System, Mechanics problem, DAE of Index 2

In deTestSet: Test Set for Differential Equations

Water Tube System, Mechanics problem, DAE of Index 2

Description

The tube problem describes the water flow through a tube system, taking into account turbulence and the roughness of the tube walls.

It is an index 2 system of 49 non-linear Differential-Algebraic Equations.

Usage

tube (times = seq(0, 17.0*3600, by = 100), yini = NULL, dyini = NULL, 
      parms = list(), printmescd = TRUE, method = radau,   
      atol = 1e-6, rtol = 1e-6, maxsteps = 1e+05, ...) 

Arguments

yini	the initial (state) values for the DE system. If y has a name attribute, the names will be used to label the output matrix.
dyini	the initial derivatives of the state variables of the DE system.
times	time sequence for which output is wanted; the first value of times must be the initial time.
parms	list of parameters that overrule the default parameter values
method	the solver to use; only mebdfi available for now
maxsteps	maximal number of steps per output interval taken by the solver
atol	absolute error tolerance, either a scalar or a vector, one value for each y.
rtol	relative error tolerance, either a scalar or a vector, one value for each y,
printmescd	if TRUE the mixed error significant digits computed using the reference solution at time 1e13 are printed
...	additional arguments passed to the solver .

Details

parameter <- c(nu = 1.31e-6, g = 9.8, rho = 1.0e3, rcrit = 2.3e3, length= 1.0e3, k = 2.0e-4, d= 1.0e0, b = 2.0e2)

Value

A matrix of class deSolve with up to as many rows as elements in times and as many columns as elements in yini, plus an additional column (the first) for the time value.

There will be one row for each element in times unless the solver returns with an unrecoverable error. If yini has a names attribute, it will be used to label the columns of the output value.

Author(s)

Karline Soetaert <[e-mail]>

Francesca Mazzia

References

http://archimede.dm.uniba.it/~testset

Examples

out <- tube()
plot(out, lwd = 2, which = 1:9)
plot(out, which = "phi3.4", lwd = 2, xlim = c(10000, 60000),
 ylim = c(0.000145, 0.000185))

# compare with reference solution
max(abs(out[nrow(out),-1]- reference("tube")))    

deTestSet documentation built on Dec. 10, 2023, 3:04 a.m.