Abstract

The necessity to provide physically reasonable and mathematically sound descriptions of mechanical behaviour at different scales is without discussion. Nevertheless, for engineering design quick estimations of important quantities such as stresses and strain are needed. This is not even enough. At a larger scale, information about the overall behaviour of complex systems has to be supplied. For this reason, we need to develop computational methods which on the one hand enable a detailed material description, on the other hand allow the bridging to coarser scales without losing too much information. In the present contribution, methods such as the phase field method are combined with FE technology, and, FE technology is combined with model reduction in order to reach this goal.

Abstract

Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions

Abstract

This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

Abstract

Abstract

Selective catalytic reduction (SCR) process with urea-water solution (UWS) is often used in automotive industry to decrease emissions of nitric oxides (NO x) in the exhaust gas. In this process the urea from UWS decomposes to isocyanic acid and ammonia, where the latter is needed to increase the efficiency of the NO xreduction on the catalyst surface. Along with the advantages of using UWS several drawbacks reduce the performance of a SCR system. Incomplete decomposition of urea leads to a formation of residuals affecting the efficiency of the exhaust gas systems. Therefore, the complete decomposition of urea and homogeneous distribution of the resulting ammonia in front of the SCR catalyst represent main challenges in improving the SCR technology. In order to investigate the process of the urea decomposition a detailed chemical kinetic mechanism in the liquid phase is employed. The results are compared with a commonly used approach to model urea decomposition as an evaporation with a following decomposition reaction in the gas phase. It is shown that by using such a mechanism, the decomposition of urea and the gas phase composition with the urea decomposition products can be described more accurately. However, implementing these mechanisms in computations (in CFD approaches) requires a large amount of computational (CPU) time and memory. The method of Reaction Diffusion Manifolds (REDIMs) is implemented for the reduction of the detailed chemical kinetics in the stage of urea decomposition such that the distribution of products of the urea decomposition can be captured accurately in the gas phase with only two reduced variables instead of the 7 gas phase species of the original model.

Abstract

In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new algorithm capable to track the matching of eigenvalues when the parameters vary.

Abstract