lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present lifex-cfd, an open-source CFD solver for cardiovascular simulations based on the lifex finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and examples on how to use lifex-cfd. We verify the code through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The lifex-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments.

计算流体动力学（CFD）是心血管功能及其失调模拟的重要工具。鉴于心脏解剖结构的复杂性、血液在心脏内的流动过渡区以及血液流动与心脏功能中涉及的物理过程之间的强烈相互影响，开发准确高效的用于心血管流动的CFD求解器仍是一项极具挑战的任务。本文我们介绍了基于lifex有限元库的开源CFD求解器lifex-cfd，该求解器采用现代C++编写，并利用分布式内存并行计算。我们通过不可压缩纳维-斯托克斯方程对生理和病理条件下的血液流动进行建模，考虑了移动的心脏瓣膜、移动的区域以及向湍流状态的过渡。在本文中，我们提供了基础的数学公式、数值离散化、实现细节以及如何使用lifex-cfd的示例。通过严格的收敛分析验证了代码，并展示了其几乎理想的并行加速效果。通过一系列理想化和基于患者的血管与心脏模拟，在不同生理流动状态下，我们验证了所实现数值方法的准确性和可靠性。lifex-cfd的源代码遵循LGPLv3许可证，以确保其对于科学界的可访问性和透明度，并促进协作及进一步的开发。