Well-Posedness Of A Coupled Problem Of Local Submodel With Linear Boundary Conditions

In the numerical simulations of hemodynamics, local phenomena, such as the perturbation of flow pattern in a specific vascular region, are strictly related to the global features of the whole circulation. In[8] we have proposed a heterogeneous model which couples a Navier-Stokes model in a specific vascular region with a lumped parameters model of the remainder of circulation by the boundary condition of the interface.This is a geometrical multiscale strategy, which couples an initial-boundary value problem to be used in a specific vascular region with an initial-value-problem in the rest of the circulatory system.It has been successfully adoped to predict the outcome of a surgical operation([7,10]).In this paper,we modify the geometrical multiscale models raised in [8],and proposed a coupled model of a local submodel with linear boundary conditions.Theorical anylisis indicate that the modify model have the same posedness as the origal model while they are more convenience and for numerical processing.We especially deseribe the lumped parameters model and the parameters it involved in more detail so as to help us to understand their physical meanings and background.We also develop a iterative approach,which is based on a natural spliting of the whole problem.This method use the forward Euler method to conduct numerical processing for the coupled problem.Its reasonableness has been proved by the ralated numerical test.