A heterogeneous non-overlapping domain decomposition explicit finite volume method for a real-time hybrid process-state estimator of 3D unsteady advection-diffusion fields

Abstract

A heterogeneous, nonoverlapping domain-decomposition, explicit, finite volume method (HT-NODDE-FVM) is developed and applied to a real-time, hybrid, process-state estimator of 3D unsteady, advection-diffusion concentration fields produced by stationary or moving gas sources. The hybrid Luenberger-naive estimator uses a single, pointwise concentration measurement of the field taken onboard a sensing aerial vehicle (SAV) and computes in real-time the concentration field in the entire domain, while guiding the SAV to locations that provide optimal information to the estimator. The computational domain of interest is divided into multiple non-overlapping subdomains using a structured and uniform grid. A Luenberger estimator (or observer) in the form of a 3D advection-diffusion partial differential equation (PDE) is developed for the subdomain where the SAV resides, and a naive estimator of a similar form is developed for the remaining subdomains. The transmission conditions are used on the interfaces between adjacent subdomains for data communication. The hybrid Luenberger-naive estimator is discretized in space by the HT-NODDE-FVM with Total Variation Diminishing (TVD) and the resulting semi-discrete equations are integrated by a fourth order Runge-Kutta scheme. Continuity and flux balance transmission conditions are enforced at the interfaces of adjacent subdomains. The HT-NODDE-FVM hybrid estimator is implemented in parallel using OpenMP. Verification and error analysis of the NODDE-FVM are performed with benchmark tests that include the 3D advection PDE for various initial density distributions and the 3D advection-diffusion PDE for instantaneous gas releases under constant wind speed and eddy diffusivities for a range of Peclet numbers. Additional benchmark tests provide verification and error analysis of the HT-NODDE-FVM hybrid estimator for an instantaneous release by a stationary gas source in a large domain with constant atmospheric properties. The tests examine the impact of grid resolution, sensor model, estimation gain, and numerical data, on the L1, L2, and L∞ norms of the estimation error. Parallelization efficiency analysis of the OpenMP implementation of the hybrid estimator is also presented. The hybrid estimator is applied to the simulation of gaseous plumes from stationary and moving sources in km-scale computational domains under realistic atmospheric conditions and the results show that it achieves real-time estimation of the concentration field.