.FailureModes.NonlinearSolverFailures.SimulationFailure .FailureModes.NonlinearSolverFailures.SimulationFailureThis model describes a simple hydraulic system with a pump, followed by a valve, which fills a reservoir.
The reservoir is filled both by the pump and by an extra source. The mass flow rate of the pump w_pump is determined by a nonlinear system with five unknowns: w_pump, dp_pump, dp_valve, sqrt_dp, and p1, which basically computes the operating point of the pump as the intersection between the pump head curve and the load (valve + reservoir head) curve. Note that these curves have two intersections (see NonlinearSolverFailure3). As the level increases, w_pump is reduced, and the two intersections get closer to each other, until at time t = 268.8 they collide, making the system singular. As the level increases further due to the extra source, this system ceases to have any solution. This is a typical bifurcation pattern in nonlinear systems.
The debugger can show that the condition number of the Jacobian of the nonlinear system gets bigger and bigger as the critical time when the two operating curves become tangent to each other, suggesting that this system becomes singular for some reason. Understanding the reason why this happens requires physical insight into the model.
The model can be fixed by adding some mass storage depending on the pressure p1, in order to avoid the singularity in determining p1, and also by using a more realistic cubic curve for the pump model, so that when the limit level is reached, the solution will jump to a big negative pump flow. Again, this requires physical insight into the validity range of the implemented model.