I have a system of non-linear DAE and I noticed that the system does not converge if some of the equations are not differentiated. For example, if the control volume equation is represented as this: $V_{total} = V_1 + V_2$ The solver won't convege.
However if I differentiate the equation like this:
$ 0 = m_1(\partial v_1/\partial p)(dp/dt)+\dot{m}_2v_2+ m_2(\partial v_2/\partial p)(dp/dt)+(\dot{m}_2v_2) $
Then it does converge. I'm using DASPK on octave.
Background: The equation is part of another five equations that are used to solve the dynamics of a steam accumulator. In such a system, a metal vessel is almost half filled with liquid water and steam is occupying the top other half of the vessel. The system operates under varying pressures and the two phases (1: liquid and 2: steam) are not always in equilibrium.
The full system of equations is as follows: the Unknowns are $M_{1},M_{2},M_{1r},M_{2r},p,\dot{m}_r$ But notice that $\dot{m}_r$ is actually calculated readily from 4
$\frac{d}{dt}[M_1+M_2] = \dot{m}_f - \dot{m}_s$
$\frac{d}{dt}[M_1h_1+M_2h_2-pV_t] = \dot{m}_fh_f - \dot{m}_sh_s$
$V_{t} = V_1 + V_2$
$\frac{d}{dt}[M_{1r}+M_{2r}] = \dot{m}_{dc} - \dot{m}_r$
$\frac{d}{dt}[M_{1r}h_1+M_{1r}h_2-pV_r] = \dot{m}_{dc}h_1 - \dot{m}_sh_s\alpha_r$
$V_{r} = V_{1r} + V_{2r}$
