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Model order reduction of transport-dominated systems with rotations using shifted proper orthogonal decomposition and artificial neural networks
Kovárnová, A. ; Isoz, Martin
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
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Model order reduction for particle-laden flows: systems with rotations and discrete transport operators
Kovárnová, A. ; Isoz, Martin
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
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Simulating particle-laden flows: from immersed boundaries towards model order reduction
Isoz, Martin ; Kubíčková, Lucie ; Kotouč Šourek, M. ; Studeník, Ondřej ; Kovárnová, A.
Particle-laden flow is prevalent both in nature and in industry. Its appearance ranges from the trans-port of riverbed sediments towards the magma flow, from the deposition of catalytic material inside particulate matter filters in automotive exhaust gas aftertreatment towards the slurry transport in dredging operations. In this contribution, we focus on the particle-resolved direct numerical simulation (PR-DNS) of the particle-laden flow. Such a simulation combines the standard Eulerian approach to computational fluid dynamics (CFD) with inclusion of particles via a variant of the immersed boundary method (IBM) and tracking of the particles movement using a discrete element method (DEM). Provided the used DEM allows for collisions of arbitrarily shaped particles, PR-DNS is based (almost) entirely on first principles, and as such it is a truly high-fidelity model. The downside of PR-DNS is its immense computational cost. In this work, we focus on three possibilities of alleviating the computational cost of PR-DNS: (i) replacing PR-DNS by PR-LES or PR-RANS, while the latter requires combining IBM with wall functions, (ii) improving efficiency of DEM contact solution via adaptively refined virtual mesh, and (iii) developing a method of model order reduction specifically tailored to PR-DNS of particle-laden flows.
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Shifted proper orthogonal decomposition and artificial neural networks for time-continuous reduced order models of transport-dominated systems
Kovárnová, A. ; Krah, P. ; Reiss, J. ; Isoz, Martin
Transport-dominated systems are pervasive in both industrial and scientific applications. However, they provide a challenge for common mode-based model order reduction (MOR) approaches, as they often require a large number of linear modes to obtain a sufficiently accurate reduced order model (ROM). In this work, we utilize the shifted proper orthogonal decomposition (sPOD), a methodology tailored for MOR of transport-dominated systems, and combine it with an interpolation based on artificial neural networks (ANN) to obtain a time-continuous ROM usable in engineering practice. The resulting MOR framework is purely data-driven, i.e., it does not require any information on the full order model (FOM) structure, which extends its applicability. On the other hand, compared to the standard projection-based approaches to MOR, the dimensionality reduction utilizing sPOD and ANN is significantly more computationally expensive since it requires a solution of high-dimensional optimization problems.
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