We present a modeling framework designed for patient-specific computational hemodynamics to be performed in the context of large-scale studies. The framework takes advantage of the integration of image processing, geometric analysis and mesh generation techniques, with an accent on full automation and high-level interaction. Image segmentation is performed using implicit deformable models taking advantage of a novel approach for selective initialization of vascular branches, as well as of a strategy for the segmentation of small vessels. A robust definition of centerlines provides objective geometric criteria for the automation of surface editing and mesh generation. The framework is available as part of an open-source effort, the Vascular Modeling Toolkit, a first step towards the sharing of tools and data which will be necessary for computational hemodynamics to play a role in evidence-based medicine.

In this work we show that the flexibility of the discontinuous Galerkin (dG) discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes. Thanks to the freedom in defining the mesh topology, we propose a new h-adaptive technique based on agglomeration coarsening of a fine mesh. The possibility to enhance the error distribution over the computational domain is investigated on a Poisson problem with the goal of obtaining a mesh independent discretization.The main building block of our dG method consists of defining discrete polynomial spaces directly on physical frame elements. For this purpose we orthonormalize with respect to the L 2 -product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes. To complete the dG formulation for second order problems, two extensions of the BR2 scheme to arbitrary polyhedral grids, including an estimate of the stabilization parameter ensuring the coercivity property, are here proposed.

a b s t r a c tIn this work we investigate the use of linearly implicit Rosenbrock-type Runge-Kutta schemes to integrate in time high-order Discontinuous Galerkin space discretizations of the Navier-Stokes equations. The final goal of this activity is the application of such schemes to the high-order accurate, both in space and time, simulation of turbulent flows. Besides being able to overcome the severe time step restriction of explicit schemes, Rosenbrock schemes have the attractive feature of requiring just one Jacobian matrix evaluation per time step, thus reducing the overall computational effort. Several high-order (up to sixth order) Rosenbrock schemes available in the literature have been implemented and evaluated on benchmark test cases of both compressible and incompressible flows. For the sake of completeness, the sets of coefficients of the schemes here considered have been reported in an Appendix to the paper. An implementation of Rosenbrock schemes for systems of equations with a solution dependent block diagonal matrix multiplying the time derivative is here proposed and described in detail. This can occur, for example, if sets of working variables different from the conservative ones are used in the compressible Navier-Stokes equations. In particular, we have found useful to employ primitive variables based on the logarithms of pressure and temperature in order to ensure the positivity of all thermodynamic variables at the discrete level. The best performing Rosenbrock scheme resulting from our analysis has then been applied to the Implicit Large Eddy Simulation of the transitional flow around the Selig-Donovan SD7003 airfoil.

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