a b s t r a c tFluid-structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton-Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.

Electrical and optical emission properties of non-equilibrium atmospheric air discharges between a metal pin and a tap water anode/cathode are presented. With a water anode the discharges are of the glow type as is derived from short-exposure time plasma imaging and electrical characteristics. Additionally, the validity of extrapolated scaling laws of low pressure glow discharge supports these findings.In the case of a water cathode the plasma is filamentary in nature at the water surface. In the case of a water anode, the plasma is diffuse down to 10 ns. The timescales on which the filaments are visible in the near water cathode region and estimates of the electrical field in the cathode layer are consistent with the assumption that these filaments occur due to the electrical instability of the water surface.Spatially resolved rotational temperature measurements and dependence of the rotational temperature on current are discussed in detail. The rotational temperatures of OH and N2 in the positive column of the plasma are identical and equal to 3250 ± 250 K. A 2500 K temperature drop in the near anode region clearly shows that the water anode acts as an effective heat sink for the discharge. This indicates that apart from the electrical stabilization of the discharge by the water electrode due to its distributed resistance, a water anode also thermally stabilizes the discharge. The rotational temperature of nitrogen near the metal anode is typically two times smaller.

This paper focuses on the stability of the coupling iterations in the partitioned approach to fluid-structure interaction. Previous research has shown that the number of coupling iterations increases when the time step decreases or when the structure becomes more flexible which is explained here by Fourier error analysis of the unsteady, incompressible flow in an elastic tube. Substituting a linearized model of the structural solver into the flow solver makes the coupling more stable but is impracticable if the flow solver is a black box. Therefore the coupling iterations are stabilized by coupling with reduced-order models and Aitken underrelaxation.

Electrical and optical emission properties of a burning plasma between a liquid cathode and a metal anode are presented in this paper. The plasma has constricted contact points at the liquid cathode and is clearly filamentary in nature near the water surface.The cathode voltage drop depends on conductivity rather than pH and is significantly different for distilled water and electrolyte solutions. An acidification of the liquid due to the plasma is always observed.The rotational temperature of OH and N 2 in the bulk of the plasma is, respectively, in the range 3200-3750 K and 2500-2750 K. The rotational temperature of nitrogen near the metal anode is typically two times smaller. Electron densities near the cathode measured by Stark broadening of H β are in the range (5.5-8.0) × 10 14 cm −3 , the atomic excitation temperatures in the range 5750-7250 K. Differences in electrical and optical emission properties between the cases when distilled water and electrolyte solutions are used as cathode are discussed in detail.

SUMMARYModel reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced-order model (ROM) remains challenging. In this work, interpolation among reduced-order matrices is proposed as a means to obtain parametrized ROMs. These ROMs are fast to evaluate and solve, and can be constructed without reference to the original full-order model. Spline interpolation of the reduced-order system matrices in the original space and in the space tangent to the Riemannian manifold is compared with Kriging interpolation of the predicted outputs. A heuristic criterion to select the most appropriate interpolation space is proposed. The interpolation approach is applied to a steady-state thermal design problem and probabilistic analysis via Monte Carlo simulation of an unsteady contaminant transport problem.

Partitioned simulations of fluid-structure interaction can be solved for the interface's position with Newton-Raphson iterations but obtaining the exact Jacobian is impossible if the solvers are "black boxes". It is demonstrated that only an approximate Jacobian is needed, as long as it describes the reaction to certain components of the error on the interface's position. Based on this insight, a quasiNewton coupling algorithm with an approximation for the inverse of the Jacobian (IQN-ILS) has been developed and compared with a monolithic solver in previous work. Here, IQN-ILS is compared with other partitioned schemes such as IBQN-LS, Aitken relaxation and Interface-GMRES(R).

In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss-Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.

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