Artificial boundaries and formulations for the incompressible Navier-Stokes equations. Applications to air and blood flows.

International audienceWe deal with numerical simulations of incompressible Navier-Stokes equations in truncated domain. In this context, the formulation of these equations has to be selected carefully in order to guarantee that their associated artificial boundary conditions are relevant for the considered problem. In this paper, we review some of the formulations proposed in the literature, and their associated boundary conditions. Some numerical results linked to each formulation are also presented. We compare different schemes, giving successful computations as well as problematic ones, in order to better understand the difference between these schemes and their behaviours dealing with systems involving Neumann boundary conditions. We also review two stabilization methods which aim at suppressing the instabilities linked to these natural boundary conditions

An anisotropic fluid–solid model of the mouse heart

A critical challenge in biomechanical simulations is the spatial discretization of complex fluid-solid geometries created from imaging. This is especially important when dealing with Lagrangian interfaces, as there must be at a minimum both geometric and topological compatibility between fluid and solid phases, with exact matching of the interfacial nodes being highly desirable. We have developed a solution to this problem and applied the approach to the creation of a 3D fluidsolid mesh of the mouse heart. First, a 50 micron isotropic MRI dataset of a perfusion-fixed mouse heart was segmented into blood, tissue, and background using a customized multimaterial connected fuzzy thresholding algorithm. Then, a multimaterial marching cubes algorithm was applied to produce two compatible isosurfaces, one for the blood-tissue boundary and one for the tissue-background boundary. A multimaterial smoothing algorithm that rigorously conserves volume for each phase simultaneously smoothed the isosurfaces. Next we applied novel automated meshing algorithms to generate anisotropic hybrid meshes with the number of layers and the desired element anisotropy for each material as the only input parameters. As the meshes are scale-invariant within a material and include boundary layer prisms, fluid-structure interaction computations would have a relative error equilibrated over the entire mesh. The resulting model is highly detailed mesh representation of the mouse heart, including features such as chordae and coronary vasculature, that is also maximally efficient to produce the best simulation results for the computational resources available. 1

A multiscale modeling method incorporating spatial coupling and temporal coupling into transient simulations of the human airways

In this article, a novel multiscale modeling method is proposed for transient computational fluid dynamics (CFD) simulations of the human airways. The developed method is the first attempt to incorporate spatial coupling and temporal coupling into transient human airway simulations, aiming to improve the flexibility and the efficiency of these simulations. In this method, domain decomposition was used to separate the complex airway model into different scaled domains. Each scaled domain could adopt a suitable mesh and timestep, as necessary: the coarse mesh and large timestep were employed in the macro regions to reduce the computational cost, while the fine mesh and small timestep were used in micro regions to maintain the simulation accuracy. The radial point interpolation method was used to couple data between the coarse mesh and the fine mesh. The continuous micro solution–intermittent temporal coupling method was applied to bridge different timesteps. The developed method was benchmarked using a well-studied four-generation symmetric airway model under realistic normal breath conditions. The accuracy and efficiency of the method were verified separately in the inhalation phase and the exhalation phase. Similar airflow behavior to previous studies was observed from the multiscale airway model. The developed multiscale method has the potential to improve the flexibility and efficiency of transient human airway simulations without sacrificing accuracy.</p