We propose a computational framework for vascular fluid-structure interaction (FSI), focusing on biomechanical modeling, geometric modeling, and solver technology. The biomechanical model is constructed based on the unified continuum formulation. We highlight that the chosen time integration scheme differs from existing implicit FSI integration methods in that it is indeed second-order accurate, does not suffer from the overshoot phenomenon, and optimally dissipates high-frequency modes in both subproblems. We propose a pipeline for generating subject-specific meshes for FSI analysis for anatomically realistic geometric modeling. Unlike most existing methodologies that operate directly on the wall surface mesh, our pipeline starts from the image segmentation stage. With high-quality surface meshes obtained, the volumetric meshes are then generated, guaranteeing a boundary-layered mesh in the fluid subdomain and a matching mesh across the fluid-solid interface. In the last, we propose a combined suite of nonlinear and linear solver technologies. Invoking a segregated algorithm within the Newton-Raphson iteration, the problem reduces to solving two linear systems in the multi-corrector stage. The first linear system can be addressed by the algebraic multigrid (AMG) method. The matrix related to the balance equations presents a two-by-two block structure in both subproblems. Using the Schur complement reduction (SCR) technique reduces the problem to solving matrices of smaller sizes of the elliptic type, and the AMG method again becomes a natural candidate. The benefit of the unified formulation is demonstrated in parallelizing the solution algorithms as the number of unknowns matches in both subdomains. We use the Greenshields-Weller benchmark as well as a patient-specific vascular model to demonstrate the robustness, efficiency, and scalability of the overall FSI solver technology.
翻译:我们为血管流体结构互动提出了一个计算框架(FSI),重点是生物机械模型、几何模型和求解器技术。生物机械模型是根据统一连续配制构建的。我们强调,所选择的时间整合计划与现有的隐含FSI整合方法不同,因为它确实是第二级的准确性,没有受到过度喷射现象的影响,并且最佳地在两个子问题中消散高频模式。我们建议建立一个管道,用于为用于解剖、实时的地球模型和求解器技术的FSI分析生成特定主题的模数。与大多数直接在墙表层上运行的现有方法不同,我们的管道是从图像分割阶段开始的。随着获得高质量的表面模数,随后生成了体积模集,保证了液体子表面的边界层网块和在液-固界面中相匹配。最后,我们提出了一套非线性流和线性基质解质解技术的组合套件。在牛顿-拉夫逊的解析度模型中采用分离的算法, 将Srental-ral-rodeal 系统的两个直径解法的精度系统的精度都显示为二号。