196,157 research outputs found
Model order reduction strategies for weakly dispersive waves
No full textWe focus on the numerical modeling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator. We propose two strategies to construct reduced order models for these problems, with the main focus being the control of the overhead related to the inversion of the elliptic operators, as well as the robustness with respect to variations of the flow parameters. In a first approach, only a linear reduction strategies is applied only to the elliptic component, while the computations of the nonlinear fluxes are still performed explicitly. This hybrid approach, referred to as pdROM, is compared to a hyper-reduction strategy based on the empirical interpolation method to reduce also the nonlinear fluxes. We evaluate the two approaches on a variety of benchmarks involving a generalized variant of the BBM–KdV model with a variable bottom, and a one-dimensional enhanced weakly dispersive shallow water system. The results show the potential of both approaches in terms of cost reduction, with a clear advantage for the pdROM in terms of robustness, and for the EIMROM in terms of cost reduction
Arbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation
No full textIn the context of preserving stationary states, e.g. lake at rest and moving equilibria, a new formulation of the shallow water system, called flux globalization has been introduced by Cheng et al. (J Sci Comput 80(1):538–554, 2019). This approach consists in including the integral of the source term in the global flux and reconstructing the new global flux rather than the conservative variables. The resulting scheme is able to preserve a large family of smooth and discontinuous steady state moving equilibria. In this work, we focus on an arbitrary high order WENO finite volume (FV) generalization of the global flux approach. The most delicate aspect of the algorithm is the appropriate definition of the source flux (integral of the source term) and the quadrature strategy used to match it with the WENO reconstruction of the hyperbolic flux. When this construction is correctly done, one can show that the resulting WENO FV scheme admits exact discrete steady states characterized by constant global fluxes. We also show that, by an appropriate quadrature strategy for the source, we can embed exactly some particular steady states, e.g. the lake at rest for the shallow water equations. It can be shown that an exact approximation of global fluxes leads to a scheme with better convergence properties and improved solutions. The novel method has been tested and validated on classical cases: subcritical, supercritical and transcritical flows
Low-switching-frequency active damping methods of medium-voltage multilevel inverters
No full textHigh power converters adopted in oil and gas applications or in wind turbine applications can benefit from the introduction of medium voltage multilevel inverters, in terms of volume and efficiency. The low switching frequency lead to currents characterized by an high harmonic content despite the use of multilevel technology, hence to high filtering needs. The use of LCL-filter is the solution to limit the size and cost of inductors. However to avoid possible resonance, passive damping is adopted leading to a decrease in the efficiency. Alternative solutions consist in the use of selective resonant damping or in active damping. These solutions are reviewed in this paper. Particularly the latter are difficult to implement due to the limited sampling frequency, typically double of the switching frequency. All the solutions are compared in terms of harmonic content and losses
A Numerical Study on the Impact Behaviour of an All-composite Wing-box
No full textAbstractIn this work a numerical study on the impact behavior of an all composite wing-box is presented. The numerical analyses have been performed by means of advanced numerical models implemented in Abaqus/Explicit. The aim was to estimate the intra-laminar and inter-laminar damage behaviour in a localized area, and, by a Global-local approach, to investigate the impact influence on the overall structural behaviour. The numerical investigation of complex composite structures under several impact conditions in terms of impact position and energy can complement the experimental results potentially leading to a reduction of the experimental tests to be performed with considerable time and cost saving
Preliminary results on very high order oscillation free Residual Distribution schemes for hyperbolic systems
No full textSince a few years, the Residual Distribution (RD) methodology has become a more mature numerical technique. It has been applied to several physical problems: standard aerodynamic problems, MHD flows, multiphase flow problems, the Shallow Water equations, aeroacoustic, to give a few examples [1,2,3]. There are also interesting contributions from other groups. These schemes are devoted to steady and unsteady problems and lead to nonlinear problems. In most cases, the expected order of accuracy is second order in space (and time for non steady problems). The accuracy is obtained only if the solution of the non linear problem is obtained with enough accuracy. The RD schemes borrow features from the finite element world: they can be interpreted as a Petrov– Galerkin scheme where the test space may depend on the solution. They also borrow features from the high order TVD–like world in that the stabilization mechanism for non smooth problems is constructed by mimicking the non oscillatory mechanism of some monotone schemes without sacrificing (formal) accuracy. Since some times there is an attempt to extend them to more than second order accuracy. Early results were obtained in [4] for steady scalar problems. The expected order of accuracy (third and fourth order) was obtained in practice for smooth solutions, while the schemes were proved to be non oscillatory. However, some problems were observed by M. Ricchiuto in his PhD thesis and by M. Hubbards (Leeds). More recently, the authors hav
Extrapolated discontinuity tracking for complex 2D shock interactions
No full textA new shock-tracking technique that avoids re-meshing the computational grid around the moving shock-front was recently proposed by the authors (Ciallella et al., 2020). The method combines the unstructured shock-fitting (Paciorri and Bonfiglioli, 2009) approach, developed in the last decade by some of the authors, with ideas coming from embedded boundary methods. In particular, second-order extrapolations based on Taylor series expansions are employed to transfer the solution and retain high order of accuracy. This paper describes the basic idea behind the new method and further algorithmic improvements which make the extrapolated Discontinuity Tracking Technique (eDIT) capable of dealing with complex shock-topologies featuring shock–shock and shock–wall interactions occurring in steady problems. This method paves the way to a new class of shock-tracking techniques truly independent on the mesh structure and flow solver. Various test-cases are included to prove the potential of the method, demonstrate the key features of the methodology, and thoroughly evaluate several technical aspects related to the extrapolation from/onto the shock, and their impact on accuracy, and conservation
Shock-fitting techniques on 2D/3D unstructured and structured grids: algorithmic developments and advanced applications
No full textOver the last decades the simulations of compressible flows featuring shocks have been one of the major drivers for developing new computational algorithms and tools able to compute also complex flow configurations. Nowadays, Computational fluid dynamics (CFD) solvers are mainly based on shock capturing methods, which rely on the integral form of the governing equations and can compute all type of flows, including those with shocks, using the same discretization at all grid points. Consequently, these methods can be implemented with ease and provide physically meaningful solutions also for complex flow configurations, features particularly attractive for CFD community. Although shock capturing methods have been the subject of development and innovations for more than 40 years, they are plagued by several numerical problems due to the shocks capture process, such as discontinuities
finite-width, numerical instabilities and reduction of accuracy order in the shock downstream region, which are still unsolved and probably will never find a solution. For this reason, there is a renewed interest in shock-fitting techniques: in particular, these methods explicitly identify the discontinuities within the flow field and compute them by enforcing the Rankine-Hugoniot jump relations. Because of this modelling, shocks are represented by zero thickness discontinuities, so that significant advantages can be gained in terms of solution quality and accuracy improvements. Furthermore, this class of methods is immune to the numerical problems linked to shock capture process. Following this research line, the presented Thesis proposes new developments
and advanced applications of shock-fitting techniques, which prove that these methods are an effective option regarding shock capturing ones in simulating flows with shocks, able to provide also a better understanding of all the phenomena linked to shock waves
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