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Completed TRL 3 (started at 2, targeting 4)
Project Objective
The main objective is to determine the optimum time step for a stable and accurate numerical simulation of a fluid transient by using NASA/MSFC's Generalized Fluid System Simulation Program (GFSSP).
Project Description
An adaptive time step second-order backward difference formula (BDF2) scheme for network flow problems has been developed and integrated into a network flow simulation software [Generalized Fluid System Simulation Program (GFSSP)] based on the finite volume method. The time step selection algorithm uses linear feedback control technique based on proportional integral derivative (PID) via a monitoring function. The monitoring function is defined by comparing a measure of the local variability of the solution. In other words, the adaptive strategy monitors the changes in key variables in two subsequent time steps. It is used to automatically adjust the step size, as the calculation progresses until user-specified tolerance bounds for the introduced monitor function are fulfilled. To assess the performance of the adaptive time stepping algorithm, it is used to predict pressure surges in a pipeline that has entrapped air at one end of the pipe. Numerical predictions are compared with available experimental data and are found to be in good agreement. Numerical experiments with adaptive BDF2 show savings in central processing unit (CPU) time in long time simulations.
Project Results and Conclusions
The proposed numerical method’s ability to accurately predict fluid transients has been demonstrated in predicting the pressure surges in a pipeline that has entrapped air. The variable time step BDF2 method predicts the pressure history not only accurately but also with reduced computational time. Furthermore, the numerical experiments further indicate that the adaptive BDF2 is less sensitive to number of branches used in the GFSSP model compared to its first-order counterpart BDF1. It can be concluded from this analysis that in general, the adaptive BDF2 algorithm is more efficient than the one that uses the constant step size advancing formula.
This technique will reduce the computational time of numerical simulation of a long transient and also will eliminate the need of performing a time step sensitivity study to determine the optimum time step.
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