The nonlinear character of the primary bifurcation is investigated for the flow around a flexibly mounted circular cylinder. We have considered the cases in which the cylinder can oscillate in the transverse direction only and in both transverse and in-line directions. Low and high values of mass ratio ($m^{\ast }=5$ and 50) were studied, and reduced velocity ($V_{r}$) values are chosen inside ($V_{r}=9$) and outside ($V_{r}=5$ and $V_{r}=13$) the lock-in range for low Reynolds numbers. For each combination of $m^{\ast }$ and $V_{r}$, a global linear stability analysis was applied to find the critical Reynolds number $Re_{c}$ of the fluid–structure system. For $V_{r}$ in the lock-in range, the values of $Re_{c}$ were noticeably less than the critical Reynolds number of the flow around a fixed circular cylinder ($Re_{c_{0}}\cong 47$). On the other hand, for $V_{r}$ outside the lock-in range, the values of $Re_{c}$ were close to $Re_{c_{0}}$. Next, nonlinear analyses were performed in the vicinity of $Re_{c}$ for each case. Subcritical character (with hysteresis) was observed for $V_{r}$ in the lock-in range, while for $V_{r}$ outside the lock-in region the bifurcations were found to be supercritical (without hysteresis). This shows that when the coupling between the structure and flow is strong, due to the proximity of the natural frequencies of the isolated systems, it significantly changes both the linear and nonlinear responses observed.
This work explores an alternative approach to computing sensitivity (derivatives) of functionals with respect to a broader range of control parameters in fluid flow problems. It builds upon the complementary character of the boundary problems that underlie the flow and the corresponding adjoint equations. Such complementarity is used to ensure well-posedness of the latter, which then yields a solution that conveys information on a broad range of sensitivities. This formulation of the boundary problem can extend the range of applications of the adjoint method to a host of new possibilities. The methodology is applied to internal and external laminar steady flows and the results are compared to those obtained with a finite-difference approach. Good agreement is observed in all cases, which demonstrates the correctness and applicability of the method.
Abstract. Full-waveform inversion (FWI) is a high-resolution numerical technique for seismic waves used to estimate the physical characteristics of a subsurface region. The continuous problem involves solving an inverse problem on an infinite domain, which is impractical from a computational perspective. In limited area models, absorbing boundary conditions (ABCs) are usually imposed to avoid wave reflections. Several relevant ABCs have been proposed, with extensive literature on their effectiveness on the direct wave problem. Here, we investigate and compare the theoretical and computational characteristics of several ABCs in the full inverse problem. After a brief review of the most widely used ABCs, we derive their formulations in their respective adjoint problems. The different ABCs are implemented in a highly optimized domain-specific language (DSL) computational framework, Devito, which is primarily used for seismic modelling problems. We evaluate the effectiveness, computational efficiency, and memory requirements of the ABC methods, considering from simple models to realistic ones. Our findings reveal that, even though the popular perfectly matching layers (PMLs) are effective at avoiding wave reflections at the boundaries, they can be computationally more demanding than less used hybrid ABCs. We show here that a proposed hybrid ABC formulation, with nested Higdon's boundary conditions, is the most cost-effective method among the methods considered here, for being as effective as or more effective than PML and other schemes but also for being computationally more efficient.
Resumo: Neste trabalho será apresentada uma aplicação do modelo algébrico PTT no problema de uma gota viscoelástica incidindo numa superfície rígida (impacting drop). A implementação e obtenção dos resultados numéricos foram feitos em uma plataforma de programação de alto desempenho denominada FREEFLOW-2D. A formulação do modelo algébricoé exposta, destacando-se os principais conceitos para sua obtenção. A metodologia empregada para resolver o modelo algébrico PTTé baseada no método GENSMAC estendido para escoamentos viscoelásticos utilizando a discretização por diferenças finitas em uma malha deslocada. A verificação dessa metodologiaé feita na simulação de um escoamento totalmente desenvolvido em um canal, comparando os resultados da solução numérica com a solução analítica. Como aplicação de escoamentos com superfície livre, o modelo algébrico foi testado na simulação de uma gota viscoelástica em uma placa rígida. Os resultados numéricos foram comparados com os previstos pelo modelo diferencial PTT, apresentando uma boa concordância. Palavras-chave: Equação constitutiva PTT, modelo algébrico, impacting drop. * Bolsista de mestrado FAPESP.
In this paper, a methodology to calculate the sensitivity of the least stable modes of fluidstructure interaction systems with respect to local forces is presented. We make use of the adjoint equations of the flow-structure coupled system to calculate the gradients, and the algorithms were implemented using the spectral/hp element method for the spatial discretization. The methodology was applied to two-dimensional incompressible laminar steady flows around an elastically-mounted circular cylinder, and we obtained the gradients of the real and imaginary parts of the least stable eigenvalues with respect to forces located at arbitrary points in the flow domain. Selected values of mass ratio and reduced velocity were considered in the simulations, and the results were compared to those obtained for a fixed cylinder at the same Reynolds number. We noticed that the sensitivity fields of the fluid-structure interaction system can be very different from its fixed structure counterpart, and amongst the cases, with an elastic structure, the fields vary greatly according to the reduced velocity. Finally, the sensitivity results were verified against linear and nonlinear simulations of flows with small control cylinders placed at locations selected according to the sensitivity fields. The agreement between the predictions made with the sensitivity analyses and the linear and nonlinear results of the forced flows was excellent. In some cases, it was possible to completely suppress the cylinder vibration.
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