Vortex structure and strength of secondary flows in model aortic arches

Abstract

SUMMARYA numerical method is developed to study the ow structures in the aortic arch. The method solves the incompressible Navier-Stokes equations. It uses a third-order upwind scheme for the convective terms and the second-order central scheme for the viscous terms. A DDADI time integration is used for achieving fast convergence. For the unsteady solutions, the second-order Crank-Nicolson method coupled with the diagonalized diagonal dominated alternating direction implicit scheme (DDADI) time integration are used. The numerical results show that the method is about 2.5-order accuracy in space and 1.8-order accuracy in time. Then the method is used to investigate the vortex structure and strength of secondary ows in the aortic arch. Four di erent arch geometries are constructed to see the e ect of arch conÿguration. Many ow properties such as pressure drop, vortex strength and separation are computed and compared among the four arch models.

A pressure correction‐volume of fluid method for simulation of two‐phase flows

“…The incompressible Navier-Stokes equations, (1a) and (1b), are solved by a pressure correction method. And, the advection equation, (1c), is solved by a third-order modified MUSCL scheme (monotone upwind scheme for conservation law) to obtain the density at the next time step [10][11][12]. To sharpen the interface, a slope modification scheme is used [13].…”

“…In this paper, the advection equation is solved by a higher order upwind scheme which is based on a modified Osher-Chakravarthy MUSCL scheme (monotone upwind scheme for conservation law) [10][11][12]. It is a third-order accurate and stable scheme to handle the compressible flows.…”

“…To compute the numerical flux by using the local Lax-Friedrich flux scheme, one needs to interpolate (or extrapolate) to obtain flow variables at the interface. A higher order upwind-biased MUSCL scheme is used [10][11][12] (For simplicity, we introduce the interpolation in the i-direction and drop the subscripts j and k in the following Equations (3)- (8)):…”

“…A modified MUSCL scheme is used to compute the volume fraction function of the advection equation (1c) [10][11][12]. It is a third-order accurate and stable scheme to handle the compressible flow.…”