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TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Papáček, Štěpán; Matonoha, Ctirad
2023 - English
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
Keywords:
Dynamical system; Singular perturbation; Averaging; Parameter estimation; Slow-fast decomposition; Damped oscillations
Fulltext is available at external website.
TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular ...
Different Boundary Conditions For LES Solver PALM 6.0 Used for ABL in Tunnel Experiment
Řezníček, Hynek; Geletič, Jan; Bureš, Martin; Krč, Pavel; Resler, Jaroslav; Vrbová, Kateřina; Trush, Arsenii; Michálek, Petr; Beneš, L.; Sühring, M.
2023 - English
We tried to reproduce results measured in the wind tunnel experiment with a CFD simulation provided by numerical model PALM. A realistic buildings layout from the Prague-Dejvice quarter has been chosen as a testing domain because solid validation campaign for PALM simulation of Atmospheric Boundary Layer (ABL) over this quarter was documented in the past. The question of input data needed for such simulation and capability of the model to capture correctly the inlet profile and its turbulence structure provided by the wind-tunnel is discussed in the study The PALM dynamical core contains a solver for the Navier-Stokes equations. By default, the model uses the Large Eddy Simulation (LES) approach in which the bulk of the turbulent motions is explicitly resolved. It is well validated tool for simulations of the complex air-flow within the real urban canopy and also within its reduced scale provided by wind tunnel experiments. However the computed flow field between the testing buildings did not correspond well to the measured wind velocity in some points. Different setting of the inlet boundary condition was tested but none of them gave completely developed turbulent flow generated by vortex generators and castellated barrier wall place at the entrance of the aerodynamic section of the wind tunnel.
Keywords:
large eddy simulation; wind tunnel; atmospheric boundary layer; PALM model; turbulence
Fulltext is available at external website.
Different Boundary Conditions For LES Solver PALM 6.0 Used for ABL in Tunnel Experiment
We tried to reproduce results measured in the wind tunnel experiment with a CFD simulation provided by numerical model PALM. A realistic buildings layout from the Prague-Dejvice quarter has been ...
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric
Kaňková, Vlasta
2023 - English
Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved on the data base. Point estimates of an optimal value and estimates of an optimal solutionset can be obtained by this approach. A consistency, a rate of convergence and normal properties, of these estimates, have been discussed (many times) not only under assumptions of independent data corresponding to the distributions with light tails, but also for weak dependent data and the distributions with heavy tails. However, it is also possible to estimate (on the data base) a confidence intervals and bounds for the optimal value and the optimal solutions. To analyze this approach we focus on a special case of static problems depending nonlineary on the probability measure. Stability results based on the Wasserstein metric and the Valander approach will be employed for the above mentioned analysis.
Keywords:
Stochastic optimization problems; static problems; empirical measure; point estimates; interval estimates; nonlinear dependence
Fulltext is available at external website.
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric
Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved ...
Improving computational efficiency of contact solution in fully resolved CFD-DEM simulations with arbitrarily-shaped solids
Studeník, Ondřej; Kotouč Šourek, M.; Isoz, Martin
2023 - English
The abundance of industrial processes containing both solid and liquid phases generate demand for fully resolved models allowing for detailed analysis and optimization of these processes. An established approach providing such models is based using a variant of an immersed boundary method to couple the computational fluid dynamics (CFD) and discrete element method (DEM). In the talk, we will present our custom and monolithic implementation of a fully-resolved CFDDEM solver and concentrate on the intricacies of solving contact between two arbitrarily-shaped solids. We shall propose an efficient contact treatment based on the concept of a virtual mesh, which provides the mesh resolution required by DEM through dividing the space around the contact point in a finite volume fashion without any changes to the CFD mesh itself. A substantial part of the talk will devoted to the parallelization of the contact solution, especially in the context of the domain decomposition method imposed by the CFD solver.
Keywords:
CFD; DEM; virtual mesh
Fulltext is available at external website.
Improving computational efficiency of contact solution in fully resolved CFD-DEM simulations with arbitrarily-shaped solids
The abundance of industrial processes containing both solid and liquid phases generate demand for fully resolved models allowing for detailed analysis and optimization of these processes. An ...
Thermal and creep analysis of VVER-1000 reactor pressure vessel at high temperatures caused by fuel melting during severe accident
Gabriel, Dušan; Gál, P.; Kotouč, M.; Dymáček, Petr; Masák, Jan; Kopačka, Ján
2023 - English
Thermal and creep analysis of the VVER-1000 reactor pressure vessel (RPV) was performed at high temperatures caused by fuel melting during severe accident. First, the integral code ASTEC was applied simulating severe accident evolution since an initiating event up to a hypothetical radioactive release into the environment. The ASTEC outputs including the remaining RPV wall thickness, the heat flux achieved and the temperature profile in the ablated vessel wall served as boundary conditions for the consequent assessment of RPV integrity carried out with the aid of finite element method (FEM). The FEM analysis was performed including the creep behaviour of RPV material using a complex creep probabilistic exponential model with damage. The objective of the analysis was to computationally assess emergency condition and, on this basis, to propose a general methodology for evaluating the integrity of RPV at high temperatures due to fuel melting during severe accident.
Keywords:
integrity of reactor pressure vessel; severe accident; ASTEC; creep; FEM
Fulltext is available at external website.
Thermal and creep analysis of VVER-1000 reactor pressure vessel at high temperatures caused by fuel melting during severe accident
Thermal and creep analysis of the VVER-1000 reactor pressure vessel (RPV) was performed at high temperatures caused by fuel melting during severe accident. First, the integral code ASTEC was applied ...
Simulation of heterogeneously-catalyzed non-isothermal reactive flow in industrial packed beds
Hlavatý, Tomáš; Isoz, Martin; Khýr, M.
2023 - English
Packed bed reactors are the most frequently used devices to perform heterogeneously catalyzed reactions on industrial scales. An industrial real-life heterogeneous catalysis is complex process that combines fully three-dimensional mass, momentum and energy transport on several scales. In the present work, we leverage our previously developed CFD solver for non-isothermal heterogeneously catalyzed reactive flow based on the finite volume method and couple it with our\nin-house DEM-based method for preparation of random packed beds. The resulting framework is verified in the simplified cases against available analytical solutions and correlations and is used to study an industrially-relevant case of ethylene oxychlorination performed in a tubular packed bed comprising CuCl2-coated catalyst carrying particles. In particular, we compare properties of three different industrially used catalyst carrying particles: Raschig rings, Reformax, and Wagon wheels
Keywords:
CFD; OpenFOAM; non-isothermal flow
Available in a digital repository NRGL
Simulation of heterogeneously-catalyzed non-isothermal reactive flow in industrial packed beds
Packed bed reactors are the most frequently used devices to perform heterogeneously catalyzed reactions on industrial scales. An industrial real-life heterogeneous catalysis is complex process that ...
Numerical implementation of incremental minimization principle for materials with multiple rate-independent dissipative mechanisms
Frost, Miroslav; Moskovka, Alexej; Sedlák, Petr; Valdman, Jan
2023 - English
The incremental energy minimization approach is a compact variational formulation of the evolutionary boundary value problem for constitutive models of materials with a rate-independent response. Although it can be easily applied to many conventional models, its main advantages arise when applied to models with multiple strongly coupled dissipation mechanisms, where the direct construction of the coupled yield conditions and flow rules may be challenging. However, this usually requires a more complex numerical treatment of the resulting sequence of time-incremental boundary value problems resolved via the finite element method. This contribution presents, compares and discusses two genuine minimization approaches - the staggered solution procedure relying on alternating minimization and the monolithic approach employing global minimization - for an advanced constitutive model of shape memory alloys.
Keywords:
variational approach; constitutive modeling; numerical implementation
Fulltext is available at external website.
Numerical implementation of incremental minimization principle for materials with multiple rate-independent dissipative mechanisms
The incremental energy minimization approach is a compact variational formulation of the evolutionary boundary value problem for constitutive models of materials with a rate-independent response. ...
Astrophysical black holes embedded in organized magnetic fields
Karas, Vladimír
2023 - English
Large-scale magnetic fields pervade the cosmic environment where the astrophysical black holes are often embedded and influenced by mutual interaction. In thiscontribution, we outline the appropriate mathematical framework to describe magnetized black holes within General Relativity, and we show several examples of how these can be employed in the astrophysical context. In particular, we examine the magnetized black hole metric in terms of an exact solution of electro-vacuum Einstein-Maxwell equations under the influence of a non-vanishing electric charge. New effects emerge: the expulsion of the magnetic flux out of the black-hole horizon depends on the intensity of the imposed magnetic field.
Keywords:
black holes; electromagnetic fields; general relativity
Fulltext is available at external website.
Astrophysical black holes embedded in organized magnetic fields
Large-scale magnetic fields pervade the cosmic environment where the astrophysical black holes are often embedded and influenced by mutual interaction. In thiscontribution, we outline the appropriate ...
Implementation of wall functions into a hybrid fictitious domain-immersed boundary method
Kubíčková, Lucie; Isoz, Martin
2023 - English
Hybrid fictitious domain-immersed boundary method (HFDIB) is a simulation approach used in computational fluid dynamics. The approach avoids usage of complex geometry-conforming computational domains. Instead, a simple domain is used and the geometry is projected onto it by a scalar field and adjustment of governing equations. Hence, the time spent on mesh generation is substantially reduced. It is advantageous to use the HFDIB in geometry optimizations where it allows for a massive optimization speed-up. Nevertheless, there is a problem with simulation of the fluid behavior in the boundary layer in the vicinity of the immersed walls. Especially, in simulation of highly turbulent flows, where the boundary layer is very thin and the usage of finer mesh is unaffordable. In this work, we aim to solve this problem by implementation of Reynolds averaged turbulence models in our custom HFDIB variant. In particular, we implemented the k-ω turbulence model and blended wall functions for closure variables and velocity.
Keywords:
wall functions; immersed boundary method; CFD; RAS
Fulltext is available at external website.
Implementation of wall functions into a hybrid fictitious domain-immersed boundary method
Hybrid fictitious domain-immersed boundary method (HFDIB) is a simulation approach used in computational fluid dynamics. The approach avoids usage of complex geometry-conforming computational domains. ...
Model order reduction of transport-dominated systems with rotations using shifted proper orthogonal decomposition and artificial neural networks
Kovárnová, A.; Isoz, Martin
2023 - English
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.
Keywords:
model order reduction; CFD; shifted POD
Fulltext is available at external website.
Model order reduction of transport-dominated systems with rotations using shifted proper orthogonal decomposition and artificial neural networks
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 ...
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