Multi-Level quasi-Newton methods for the partitioned simulation of fluid-structure interaction

In previous work of the authors, Fourier stability analyses have been performed of Gauss-Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time

Diophantine sets of polynomials over algebraic extensions of the rationals

Let L be a recursive algebraic extension of Q. Assume that, given alpha is an element of L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to alpha. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of alpha, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in a finite extension of Q(p) (with p an odd prime). Then we show that subsets of L[X](k) that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X]

Hilbert's Tenth Problem for rational function fields over p-adic fields

Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate "v_t(x) >= 0" in K(t). This implies undecidability of diophantine equations over K(t)

A study of the vibration of a horizontal U-bend subjected to an internal upwards flowing air-water mixture

U-bends are a common geometry in heat exchangers. In this paper, a U-bend in the vertical plane connected to horizontal straight pipes is considered. An initially stratified water/air flow moves upwards against gravity. The aim of this research is to investigate the internal flow profile and resulting force when the U-bend is subjected to a stratified air-water flow at the inlet. This is done numerically, i.e. by solving the unsteady Reynolds-averaged Navier-Stokes equations. For low mass flow rates, large gas bubbles are naturally formed at the entrance of the bend. The transient force on the tube allows to determine precisely the time instants of bubble initiation and thus to quantify the bubble frequency. Firstly, the tube is assumed to be rigid and the dependence of force oscillation on the inlet conditions is investigated. Secondly, the influence of the viscosity, wall wetting and the mass flow rate is analyzed. Finally, a fluid-structure interaction calculation is performed in order to quantify the vibration characteristics of the tube

Numerical and analytical investigation of subcycling in the flow problem of a strongly-coupled partitioned fluid-structure interaction simulation

Fluid-structure interaction (FSI) simulations can be used to quantify the frequency, damping constant and amplitude of the vibration of equipment such as piping and heat exchangers. Typically, the time step is the same in the flow and structural equations, but this causes long computational times when the time step is restricted due to stability requirements of only one solver. In that case, a more efficient approach is to use so-called subcycling with a different time step in the flow and structural solver. In this paper, only subcycling with a smaller time step in the flow solver compared to the structural solver is analyzed. The research presented here is split into two parts: an analytical study and a numerical computation of the one-dimensional flow in an elastic cylindrical tube. Firstly, a monolithic analytical FSI calculation is analyzed with a Fourier stability analysis. This allows to verify the stability of the solution by considering the eigenvalues of the problem as a function of the perturbation wavenumber. The conclusions drawn from the analytical study are subsequently verified in a partitioned numerical FSI simulation, coupling the flow solver Fluent with the structural solver Abaqus. The implicit coupling is achieved using an interface quasi-Newton method with an approximation of the inverse of the Jacobian (IQN-ILS), implemented in the in-house code Tango. The research shows that a stable solution is attained for significant subcycling in the flow problem: the results indicate that the solution remains temporally stable even if the time step in the flow solver is only one tenth of the structural time step. However, some (temporally stable) oscillations in the resulting pressure profile on the pipe wall arise when the time discretization schemes applied in the flow and structural solvers are different.These oscillations do not persist when the same time discretization scheme is applied

What determines health-related quality of life among people living with HIV : an updated review of the literature

Background: As infection with the Human Immunodeficiency Virus (HIV) has evolved to a chronic disease, perceived health-related quality of life (HRQoL) is becoming a prominent and important patient-reported outcome measure in HIV care. Literature discusses different factors influencing HRQoL in this population, however, currently no consensus exists about the main determinants. In this review a clear, up-to-date overview of the determinants influencing HRQOL among people living with HIV is provided. Methods: All studies published before July 2013 that identified determinants of HRQoL among people living with HIV in high-income countries, were considered in this narrative review. PubMed, Web of Science and The Cochrane Library were consulted using the keywords ‘determinants’, ‘quality of life’, ‘HIV’ and ‘AIDS’. To be included, studies should have reported overall health and/or physical/mental health scores on a validated instrument and performed multivariable regression analyses to identify determinants that independently influence perceived HRQoL. Results: In total, 49 studies were included for further analysis and they used a variety of HRQoL instruments: Medical Outcomes Study Short Form-36 or variants, Medical Outcomes Study-HIV, HIV Cost and Services Utilization Study measure, Multidimensional Quality of Life Questionnaire, HIV targeted quality of life instrument, Functional Assessment of Human Immunodeficiency Virus Infection, HIV Overview of Problems Evaluation System, EuroQol, Fanning Quality of Life scale, Health Index and PROQOL-HIV. In this review, the discussed determinants were thematically divided into socio-demographic, clinical, psychological and behavioural factors. Employment, immunological status, presence of symptoms, depression, social support and adherence to antiretroviral therapy were most frequently and consistently reported to be associated with HRQoL among people living with HIV. Conclusions: HRQoL among people living with HIV is influenced by several determinants. These determinants independently, but simultaneously impact perceived HRQoL. Most HRQoL instruments do not capture all key determinants. We recommend that the choice for an instrument should depend on the purpose of the HRQoL assessment

Evaluation of a new implicit coupling algorithm for the partitioned fluid-structure interaction simulation of bileaflet mechanical heart valves

The movement of the leaflets of Bileaflet Mechanical Heart Valves (BMHVs) strongly interacts with the surrounding fluid motion and therefore it needs to be modeled through a Fluid-Structure Interaction (FSI) scheme with implicit coupling. Therefore, when using partitioned solvers, a subiteration loop within each time step is needed. The stability of such a scheme depends on the value of the under-relaxation factor. For the simulation of a BMHV, several methods can be used to find such an appropriate under-relaxation factor, like fixed under-relaxation or the dynamically changing Aitken Δ2 under-relaxation. Also, a stable scheme can be achieved with a newly developed algorithm which uses the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with resprect to the angular accelerations of the leaflets. In this paper, this new algorithm is presented and compared to existing coupling schemes. It is shown through numerical experiments that our newly developed algorithm outperforms these existing coupling schemes