High resolution methods for scalar transport problems in compliant systems of arteries

摘要: In this paper a new semi-implicit high resolution scheme for the simulation of advection-diffusion problems in compliant arterial systems is proposed. Such transport are not only great importance modeling drug delivery processes, but also continuous processes occurring human body such as exchange oxygen, carbon dioxide, nutrients and toxics. Assuming cylindrical geometry axially symmetric blood flow, finite volume scalar on unstructured staggered grids derived. It shown how both mass conservation maximum principle can be assured by present method. Since discrete imposes CFL type restriction time step, equation solved using consistent local time-stepping approach order to affect unconditional stability underlying hydrodynamics. key feature that radial profiles axial velocity concentration computed directly from first principles no heuristic model profile needed classical one-dimensional approaches, which still frequently used artery trees. The knowledge gradients fundamental happening across vessel walls. accuracy proposed validated one- two-dimensional test with exact solution. An example tree 55 branches rounds off numerical discussed paper.