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We investigate the temporal accuracy of two generalized‐ schemes for the incompressible Navier‐Stokes equations. In a widely‐adopted approach, the pressure is collocated at the time stept_n + 1while the remainder of the Navier‐Stokes equations is discretized following the generalized‐ scheme. That scheme has been claimed to besecond‐order accurate in time. We developed a suite of numerical code using inf‐sup stable higher‐order non‐uniform rational B‐spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve high spatial accuracy and to investigate asymptotic temporal convergence behavior. Numerical evidence suggests that onlyfirst‐order accuracyis achieved, at least for the pressure, in this aforesaid temporal discretization approach. On the other hand, evaluating the pressure at the intermediate time step recovers second‐order accuracy, and the numerical implementation is simplified. We recommend this second approach as the generalized‐ scheme of choice when integrating the incompressible Navier‐Stokes equations.

 

Abstract We propose svMorph, a framework for interactive virtual sculpting of patient-specific vascular anatomic models. Our framework includes three tools for the creation of tortuosity, aneurysms, and stenoses in tubular vascular geometries. These shape edits are performed via geometric operations on the surface mesh and vessel centerline curves of the input model. The tortuosity tool also uses the physics-based Oriented Particles method, coupled with linear blend skinning, to achieve smooth, elastic-like deformations. Our tools can be applied separately or in combination to produce simulation-suitable morphed models. They are also compatible with popular vascular modeling software, such as SimVascular. To illustrate our tools, we morph several image-based, patient-specific models to create a range of shape changes and simulate the resulting hemodynamics via three-dimensional, computational fluid dynamics. We also demonstrate the ability to quickly estimate the hemodynamic effects of the shape changes via automated generation of associated zero-dimensional lumped-parameter models.