Abstract. The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In Fluid-Structure Interaction (FSI, in short) for haemodynamic applications, parallelization and scalability are key issues (see [20]). In this work we introduce a class of parallel preconditioners for the FSI problem obtained by exploiting the block-structure of the linear system. We stress the possibility of extending the approach to a general linear system with a block-structure, then we provide a bound in the condition number of the preconditioned system in terms of the conditioning of the preconditioned diagonal blocks, finally we show that the construction and evaluation of the devised preconditioner is modular. The preconditioners are tested on a benchmark 3D geometry discretized in both a coarse and a fine mesh, as well as on two physiological aorta geometries. The simulations that we have performed show an advantage in using the block preconditioners introduced and confirm our theoretical results.Key words. Blood-Flow Models , Fluid-Structure Interaction , Finite Elements , Preconditioners , Parallel Algorithms AMS subject classifications. 65M60 , 65F08 , 65Y05 , 76Z051. Introduction . The modeling of the cardiovascular system is receiving increasing attention from both the medical and mathematical environments because of, from the one hand, the great influence of haemodynamics on cardiovascular diseases ([20] chap 1), and, from the other hand, its challenging complexity that keeps open the debate about the setting up of appropriate models and algorithms. A wide variety of approaches can be found in literature, dealing with different formulations of the problem and solution strategies.In this introduction we refrain from describing the models that can be used to simulate the physiological behavior of the arterial vessels; for that we address the interested reader to [20]. We give instead an overview of some of the most popular methodologies to solve numerically the coupled system of equations arising from the haemodynamic model: those that describe the flowfield variables (blood velocity and pressure) and those that govern the mechanical deformation of the vessel walls (the "structure"). The first distinction comes from the formulation of the problem.A common choice in the FSI context is to describe the fluid equations using an Arbitrary Lagrangian-Eulerian frame of reference (see e.g. [31]). The advantage with respect to an Eulerian description is that the coupling can be satisfied exactly on the fluid-structure interface. However the introduction of a new equation for the fluid domain motion is required, and its dependence on the solution of the FSI problem introduces a further nonlinearity.A different approach consists of a space-time formulation which adopts the Eulerian framework. Usually, the latter involves a discretization of the computational domain in time slab...

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Self-consistent full-size turbulent-transport simulations of the divertor and scrape-off-layer of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted Ohmic L-mode discharges on the TCV tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from 5 diagnostic systems from the outboard midplane to the divertor targets -- giving a total of 45 one- and two-dimensional comparison observables in two toroidal magnetic field directions. The experimental dataset is used to validate three flux-driven 3D fluid-turbulence models -- GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, individually tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the outboard midplane -- both in terms of profile shape and absolute magnitude -- while a comparatively poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset and validation analysis, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and scrape-off-layer.

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