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Introduction Turbulent aortic flow has long been recognised as a symptom of aortic valve stenosis [1]. It is believed that turbulence is physiologically unfavourable in the aorta, as it correlates with elevated drag and shear stress levels. It can lead to endothelial dysfunction and blood trauma. Quantitative turbulent flow analysis, as the core concept of in-vivo, in-vitro and in-silico studies, can be directly used for valvular disease diagnosis and testing of existing prostheses. Understanding the transition process to turbulence in the aorta can further act as a cornerstone for the optimal design of aortic valve prostheses, in particular, for mechanical prostheses, for which, blood damage and coagulation are major limitations. Recent post-operative survey studies [2] report lower mortality rates and re-operation need for the recipients of mechanical prostheses, as compared to biologic ones. However, mechanical valves are connected with higher risks of post-operative trauma, such as bleeding and stroke. Preventing the turbulence in and past a mechanical prosthesis can reduce such adverse events, and offer a design with reliable performance and longevity. Methods Herein, we report our ongoing work on understanding the mechanisms of transition to turbulence in such prostheses. We resort to high-order direct numerical simulations (DNS) of systolic blood flow in the proximity of a bileaflet mechanical valve. In order to capture the unstable modes of blood motion and their interaction in the complex wall-bounded geometry of valve and sinuses, scale-resolving simulations (25 micrometer grid spacing) are performed on massive number of CPUs/GPUs of a Cray XC50 supercomputer (CSCS’s Piz Daint). Results and Discussion DNS results have unveiled critical vortex shedding on the valve leaflets. It becomes evident only by ultra- high resolutions that there exists a stagnation point on the leaflet’s thin leading attachment surface. (Figure 1). The significant transverse flow near the leading edge forms a vortex which elongates over the leaflet’s inner side by gaining systolic momentum and eventually separates at a second stagnation point on the leaflet. Vortices are then shed and grow spatially as they move downstream. Such boundary layer modes then appear to interact with Burger vortices developing at the trailing edge of the leaflets. This interaction seems to trigger transition to turbulence. In contrast, the outer sides of the valve leaflets, feature stable Falkner-Skan type boundary layers. In order to study the critical inter-leaflet instabilities, linear stability theory is locally applied. Efforts are then made towards suppressing such unstable modes, predicted by hydrodynamic stability theory. References [1] Roberts, W.C., et al., 1971, The American journal of cardiology, 27(5), pp.497-506. [2] Goldstone, A.B., et al., 2017, New England Journal of Medicine, 377(19), pp.1847-1857.

A GPU-accelerated high-order massively-parallel 3D Navier-Stokes solver has been developed for heart valve simulation. It is optimized for a Cray XC50 supercomputer by distributing the workload to different MPI processes and by offloading double-precision kernels to GPUs. The GPU kernels are written in CUDA C and are called by the FORTRAN legacy code. For a high-order finite-difference gradient kernel speedups of 5x (Tesla K20x) and 20x (Tesla P100) were achieved. In combination with 16 MPI threads on a single node of the Cray XC50, a peak speedup of 33x was achieved using CUDA MPS. Similar performance was also achieved for other differential operators, demonstrating the potential of GPU technology for bringing biomedical CFD to exascale computing.

Immersed boundary methods have become the most usable and useful tools for simulation of biomedical fluid-structure interaction, e.g., in the aortic valve of human heart. In such problems, complex geometry and motion of the soft tissue impose significant computational cost for bodyfitted- mesh methods. Resorting to a fixed Eulerian grid for the flow simulation along with the immersed boundary method to model the interaction with the soft tissue eliminates the expensive mesh generation and updating costs. Nevertheless, the computational cost for the geometry operations including adaptive search algorithms are still significant. Herein, we implemented the immersed boundary kernels with CUDA to be transferred and executed on thousands of parallel threads on the general purpose GPU. Host-device memory optimisation along with optimal usage of GPU multiprocessors results in a boosted performance in fluid-structure interaction simulation.

Viskoelastik bir damlacığın kompleks geometrilerdeki hareketi ve dinamiğinin doğrudan sayısal simülasyonu için bir daldırılmış sınır yöntemi geliştirildi ve mevcut sonlu-farklar/ara-yüz izleme metoduyla birleştirildi. Bu yaklaşımda, akış ve viskoelastik model denklemleri sınırla uyumlu olmayan Kartezyen bir çözüm ağı üzerinde çözülürken sınır şartları daldırılmış sınır yöntemi kullanılarak uygulanmaktadır. Bu amaçla ilk olarak katı bölgesinde kalan ve akışkan bölgesiyle komşu olan gölge çözüm ağı hücreleri hesaplamalı geometri yöntemleriyle tespit edilmekte ve daha sonra ise bu gölge çözüm ağı hücreleriyle ilintili olan akışkan tarafındaki imaj noktaları ve akışkan-katı sınırındaki kesişim noktaları tespit edilmektedir. Gölge çözüm ağı hücrelerindeki akış büyüklükleri imaj noktalarındaki değerler ve sınır şartları kullanılarak hesaplanmaktadır. İmaj noktalarındaki akış büyüklükleri ise lineer interpolasyon kullanılarak hesaplanmaktadır. Karışamayan akışkanların ara-yüzeyi ise ayarı bir Lagrangian çözüm ağı vasıtasıyla temsil edilmektedir. Lagrangian çözüm ağı işaretleme noktalarından oluşmakta olup bu işaretleme noktaları yerel akış hızıyla hareket etmektedir. Yöntem ilk olarak tek fazlı Newtonsal bir akışkanın daralan-genişleyen bir kanaldaki basınç tahrikli akışı için test edilmiş, sonuçların ticari Fluent yazılımı sonuçlarıyla iyi bir uyum içinde olduğu gösterilmiştir. Yöntem daha sonra Newtonsal bir damlacığın başka bir Newtonsal akışkanla dolduruluş ve sinüsoidal olarak daralıp-genişleyen kanaldaki basınç tahrikli akıştaki hareket ve deformasyonu için test edilmiş ve sonuçların Tsai ve Miksis (1994) sınır-eleman yöntemi sonuçlarıyla iyi bir uyum içerisinde olduğu gösterilmiştir. Son olarak viskoelastik bir damlacığın iki farklı daralan-genişleyen kanaldaki basınç-tahrikli hareketi ve deformasyonu incelenmiştir. Viskoelastisite yalnızca damalcık sıvısı içerindedir ve viskolelastik etkiler FENE-CR modeli kullanılarak hesaba katılmıştır. Weissenberg, kapillari ve Reynolds sayışlarının etkilerini araştırmak için çok sayıda sayısal simülasyon yapılmıştır. Simülasyonlar büyük oranda sinusoidal olarak daralıp-genişleyen kanalda yapılmış ama yöntemin daha zor olan keskin kenarlı daralan-genişleyen kanallar içinde çalıştığı da ayrıca gösterilmiştir. Viskoelastisitenin damlacık dinamiği üzerindeki etkilerin son derece kompleks ve nonlineer olduğu gösterilmiştir. Damlacık deformasyonun zayıf viskoelastik durumda azalırken yüksek viskoelastisite durumunda arttığı görülmüştür. Viskoelastik etkiler en çok daralma bölgesinde görülmektedir. Damlacık deformasyonunun genel olarak kapilari sayısı, Reynolds sayısı, kanal daralma oranı ve göreceli damlacık büyüklüğü ile arttığı tespit edilmiştir. A sharp interface immersed boundary method is developed and coupled with afinite-difference/front-tracking algorithm for direct numerical simulations of viscoelasticdrops in complex capillaries. In this approach, the flow equations are solved on a non-body conforming Cartesian grid and the boundary conditions are imposed along thefluid-solid interface using an immersed boundary method. For this purpose, the ghostcells are first identified through computational geometry operations in the preprocessingstage and then employed to impose the boundary conditions on the solid boundaryusing the image point methodology at each time step. The method incorporatesbilinear interpolation to maintain the overall second order spatial accuracy of thenumerical method. The fluid-fluid interface is represented by a separate Lagrangiangrid using a conventional front-tracking technique. The method is first validated for asingle phase Newtonian fluid flow through a pressure-driven constricted channel andthe results are found to be in good agreement with the results obtained using a body-conforming mesh method in the commercial Fluent software package. The method isalso validated for a bubble moving through a constricted capillary tube filled with aNewtonian liquid and the results are found to be in good agreement with those of Tsaiand Miksis (1994). Finally, the method is used to study the effects of viscoelasticityon drop dynamics in complex geometries. The viscoelasticity is contained only in thedrop fluid and accounted for using the FENE-CR model. Extensive simulations areperformed to examine the effects of various flow parameters including the Weissenbergnumber (Wi), the capillary number (Ca), the Reynolds number (Re) and the relativedrop size (κ) on the drop deformation and dynamics. Simulations are also performedfor different constriction profiles such as a sharp-edged protrusion. It is found thatthe viscoelasticity influences drop dynamics in a complicated and non-monotonic way:The deformation is surpassed by increasing the Weissenberg number in weakly elasticsystems, however, the viscoelasticity enhances the drop deformation after a certainWeissenberg number which depends on drop size. The viscoelastic effects are morepronounced in the constriction region due to intense shearing. It is also found thatdrop deformation is strongly influenced by and generally increases with the capillarynumber, the Reynolds number, the constriction ratio and the relative drop size. 92