Stability of Dynamic Fluid Transport Simulations with Mixing Flows

This work presents physically based simulation of energy distribution and substance composition for dynamic fluid transport problems. The main addressed problem is the stability of the algorithms for solving the resulting systems of differential-algebraic equations. The challenges encountered include system degeneration, the appearance of stochastic degrees of freedom, jumps in thermodynamic functions during phase transitions, and proper scaling of equations. The proposed solution is the identification and optimal configuration of solver parameters, strongly affecting the stability and speed of the simulation. Such parameters include regularizing and weighting constants, dimensioning of dynamic terms and startup procedure, the size of the integration step and their total number. The main output of the paper is the optimal choice of these parameters that allows to speed up significantly the dynamic simulation of fluid transport for realistically large network scenarios.