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Applied Math Colloquium

Friday, February 1, 2013, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Simulating fluid flow and solute transport in a compliant tube

Anita Layton

Department of Mathematics, Duke University

Abstract

We present a hybrid numerical method for simulating fluid flow through a compliant closed tube, driven by an internal source and sink. Fluid motion is described by the Navier-Stokes equations, with a singular force due to the stretching of the moving tubular interface. Model geometry is assumed to be axisymmetric, and the governing equations are implemented in axisymmetric cylindrical coordinates, which capture 3D flow dynamics with only 2D computations. To solve the model equations, we decompose the velocity into a ``Stokes'' part and a ``regular'' part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier-Stokes equations, a body force resulting from the Stokes part, and the sink and source terms. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. Numerical results are presented that indicate second-order accuracy of the method. The model is used to simulate the transport of nitric oxide along an afferent arteriole. Nitric oxide is a vasodilator, whereas the afferent arteriole exhibits the myogenic response, by which the vessel constricts in response to an increase in hydrostatic pressure.