A comparison of numerical integration schemes for particle filter-based estimation of gas flow dynamics

Abstract

In this paper, we endeavor to find a fast and robust time integration solver for estimating gas flow transients within the framework of particle filtering. We examined both stiff and nonstiff solvers, namely embedded explicit Runge–Kutta (ERK) schemes based on Dormand–Prince, a second-order diagonally implicit RK (DIRK) scheme, a Krylov–Rosenbrock method using a multiple Arnoldi process and an implicit RK scheme with coefficients from Radau IIA quadrature formulas. Issues of accuracy, robustness and computation time, but also the stiffness of the problem were addressed. As well as comparing the performance of the time-stepping schemes for multiple model realizations in the particle filter, the analysis was also completed for a single noise-free model integration. Numerical experiments showed that the DIRK scheme is most robust whereas the ERK schemes were superior in terms of efficiency if the grid density and tolerance were properly selected. Under certain circumstances, nonphysical oscillations might appear in the solution domain. Stiffness measures and superior efficiency of the ERK schemes indicate that the problem can be considered as nonstiff.