Fluid-structure Interaction Parallel Numerical Simulation For Human Hemodynamics In Three-Dimensional Unstructured Grid

Cardiovascular disease is a major disease that endangers the safety of human lives and property,which is still the most lethal one.Therefore,prediction and treatment of cardiovascular disease is an important and urgent project.The majority of ischemic cardiovascular disease is caused by atherosclerosis,whose production and development are closely related to the human hemodynamics,additionally the current diagnosis and treatment of cardiovascular diseases are also mainly focused on the hemodynamics aspect.With the development of computer technology,the use of numerical calculation to solve the problem related to hemodynamics has become a hot research content.The combination of hemodynamics and medical diagnosis and treatment of cardiovascular disease not only provides doctors with scientific and objective pathological judgment,but also plays a very important role in the prediction and prevention of major diseases.On human hemodynamics,many studies are based on the assumption that the vascular wall is rigid,and the research model is mostly a simple ideal model.There were many foreign studies considering the vascular wall as elastic wall,and giving the corresponding Fluid-Structure Interaction(FSI)high performance algorithm,but many are based on structured grid,which has low applicability due to the complex vascular geometry model and physics process.From this point,it is a great challenge to achieve true and efficient rapid simulation of human hemodynamics.It is Cai that proposed a fully coupled Newton-Krylov-Schwarz(NKS)algorithm based on unstructured grids,which has a good effect on the treatment of the FSI model of blood flow.However,the algorithm could not be applied directly to the real brain for solving the problem of vascular model.In order to solve the problem of numerical simulation of real human cerebrovascular FSI model,we propose a fully implicit and coupled high-scalable parallel algorithm based on unstructured grid,which mainly includes the following three aspects:1.We studied the FSI mathematical model and discrete format based on human hemodynamics.In addition to the most important regions of blood fluid,the human hemodynamic model has a linear elastic vascular wall solid region and a moving mesh section for moving mesh analysis.The FSI interface plays the role of variable delieveing and data mapping.For the whole FSI model,we establish the linear elastic equation of the solid part with Lagrange reference system,the incompressible NS Equation with ALE framework and fluid grid motion harmonic equation.We optimized the linear elastic equation in the FSI mathematical model,emphasizing the effect of the viscoelastic damping coefficient on the correct calculation of the real cerebral vascular model.The FSI problem we studied is a time-dependent transient problem that needs to be spatially and temporally separated at the same time.By the finite element method in space and the second order implicit discrete method in time,a fully implicit discrete form of equations is constructed,which is very helpful for solving unsteady problems over long time calculation.2.We studied the parameterized NKS algorithm for solving large-scale nonlinear equations.The FSI mathematical model after discretization constitutes a large-scale sparse nonlinear equations,for large-scale sparse non-linear equations,the classical iterative method and the modern homotopy continuation method and Artificial Intelligence method and their deformation solution method were studied.We choose to use a class of inaccurate Newton method.Because of the existence of double-layer iteration and convenient for gain solution by using preconditioner,this algorithm has many different combination algorithms.In this paper,Newton-Krylov-Schwarz(NKS)algorithm was used to solve nonlinear equations.Based on this algorithm,the modification of the viscoelastic damping coefficient and the improvement of the convergence conditions are made to adapt to the fast and high performance solution of the FSI model of human blood flow when it comes to the real model and boundary parameters.3.We studied Schwarz parallel algorithm and total software implementation for accelerating linear iteration.The number of unknowns produced by the discretization of the problem mentioned in the paper reached millions of scale,so multi-core processors parallel method can be used to solve the problem effectively.In the paraNKS algorithm,the Schwarz algorithm for accelerating the iterative convergence of subspaces is an overlapping type of region decomposition method.The inherent parallelism of Schwarz algorithm makes it very suitable for constructing parallel algorithms for large-scale supercomputers.The processed data sources we used are CT/MRI medical image data,the three-dimensional model of blood vessels is reconstructed by Mimics,and the unstructured grids are obtained through the ICEM in the commercial software ANSYS.The ParMETIS is used to get region partition in our algorithm,calculation results obtained through above method will be post processing by Paraview.The above parallel algorithm is applied to the real three-dimensional numerical simulation of human cerebrovascular,and the model is calculated and analyzed through the real blood flow boundary conditions.Numerical results show that there is still a parallel efficiency of nearly 40% when using 8192 processor cores to solve the real cerebrovascular FSI with over 20 million mesh elements,and the algorithm has good convergence when the physics model is close to rigid wall.