A Heterogeneous Non-Overlapping Domain Decomposition Explicit Finite Volume Method for Real-Time Estimation of 3D Advection-Diffusion Fields with a Sensing Aerial Vehicle

Tian, Xin

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A Heterogeneous Non-Overlapping Domain Decomposition Explicit Finite Volume Method for Real-Time Estimation of 3D Advection-Diffusion Fields with a Sensing Aerial Vehicle

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A heterogeneous, non-overlapping domain decomposition, explicit, finite volume method (HT-NODDE-FVM) is developed to solve numerically a 3D advection-diffusion process-state hybrid estimator. The HT-NODDE-FVM is applied to real-time estimation problems of 3D unsteady advection-diffusion plume fields produced by stationary and moving sources. The field measurements are taken by a sensor onboard a guided sensing aerial vehicle (SAV). The hybrid Luenberger-naive estimator uses those field measurements to compute the plume field in real-time and guide the SAV to locations that provide optimal information to the hybrid estimator. A structured and uniform grid is used to divide the computational domain of interest into multiple non-overlapping subdomains. In the subdomain where the SAV resides, a Luenberger estimator in the form of a 3D advection-diffusion partial differential equation is used to estimate the plume field. In the remainder of the subdomains, a naive observer of a similar form is used. The transmission conditions are used on the interfaces between adjacent subdomains for data communication. The spatial discretization of the hybrid Luenberger-naive estimator is conducted by the HT-NODDE-FVM with Total Variation Diminishing (TVD). Continuity and flux balance transmission conditions are enforced at the interfaces of adjacent subdomains when conducting the FVM-TVD discretization. The resulting semi-discrete equations are integrated by a 4th order Runge-Kutta method. OpenMP parallel paradigm is implemented to parallelize the HT-NODDE-FVM estimator. The verification and error analysis of the NODDE-FVM are performed with two benchmark tests. One is the 3D advection of different initial density distributions, the other is the 3D advection-diffusion of instantaneous gaseous releases under constant wind speed and eddy diffusivities for a range of Peclet numbers. The verification and error analysis of the HT-NODDE-FVM hybrid estimator are also conducted on an instantaneous release by a stationary source in a large domain with constant atmospheric properties. The impact of grid resolution, sensor model, estimation gain, and numerical data, on the L^1, L^2, and L^∞ norms of the estimation error are examined by those test cases. Parallelization efficiency analysis of the OpenMP implementation of the hybrid estimator is also presented. Finally, the hybrid estimator and the HT-NODDE-FVM are applied to estimate the gaseous plumes released from stationary and moving sources in a km-scale computational domain under realistic atmospheric conditions and SAV parameters. Real-time estimation analysis is also conducted by comparing the wall clock time of completing an iteration over all the subdomains with the maximum allowable numerical time step for the temporal integration. The simulation results show that the hybrid estimator and the HT-NODDE-FVM can achieve real-time estimation of the advection-diffusion field in very fine grid settings.

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