Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

We present a framework for adaptive finite element computation of turbulent flow and fluid-structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for efficient parallel implementation. To illustrate the capabilities of the computational framework, we show a number of application examples from aerodynamics, aero-acoustics, biomedicine and geophysics. The computational tools are free to download open source as Unicorn, and as a high performance branch of the finite element problem solving environment DOLFIN, both part of the FEniCS project.

Writing high performance solvers for engineering applications is a delicate task. These codes are often developed on an application to application basis, highly optimized to solve a certain problem. Here, we present our work on developing a general simulation framework for efficient computation of time resolved approximations of complex industrial flow problems -Complex Unified Building cubE method (Cube). To address the challenges of emerging, modern supercomputers, suitable data structures and communication patterns are developed and incorporated into Cube. We use a Cartesian grid together with various immersed boundary methods to accurately capture moving, complex geometries. The asymmetric workload of the immersed boundary is balanced by a predictive dynamic load balancer, and a multithreaded halo-exchange algorithm is employed to efficiently overlap communication with computations. Our work also concerns efficient methods for handling the large amount of data produced by large-scale flow simulations, such as scalable parallel I/O, data compression and in-situ processing.

We present a time-resolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW-2 workshop, where this method is used to compute the flow past a DLR-F11 aircraft model at realistic Reynolds number. The mesh is automatically constructed by the method as part of the computation, and no explicit turbulence model is used. The effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of the skin friction. In the extreme case of very high Reynolds numbers we approximate the small skin friction by zero skin friction, corresponding to a free slip boundary condition, which results in a computational model without any model parameter that needs tuning. Thus, the simulation methodology bypasses the main challenges posed by high Reynolds number CFD: the design of an optimal computational mesh, turbulence (or subgrid) modeling, and the cost of boundary layer resolution. The results from HiLiftPW-2 presented in this report show good agreement with experimental data for a range of different angles of attack, while using orders of magnitude fewer degrees of freedom than what is needed in state of the art methods such as RANS.

No abstract