High-Order solver for Blood Flow Using WENO Scheme

摘要

A high order solver for the blood flow is developed and analyzed using a two-dimensional backward-facing step.In the first part, a Newtonian steady code to solve the incompressible Navier-Stokes (N-S) equations has been developed. The accuracy of the code is verified by the experimental results. An exact projection method/fractional-step scheme is used to solve the incompressible N-S equations. Convective terms of the N-S equations are solved using fifth-order WENO spatial operators, and for the diffusion terms, asixth- order compact central difference scheme is employed.The use of WENO scheme is advantageous as it captures the general features of the flow with coarse grid. The third-order Runge-Kutta (R-K) explicit time-integrating scheme with total variation diminishing (TVD) is adopted for time discretization.In the second part, the pulsatile behavior of the Newtonian blood flow has been added to the initial program. Finally, the numerical code has been extended to include the steady and pulsatile effects in non-Newtonian blood flow.