| Abstract: | We have developed a numerical method for simulating viscous flow through a compliant closed tube, driven by a pair of fluid source and sink.As is natural for tubular flow simulations, the problem is formulated in axisymmetric cylindrical coordinates, with fluid flow described by the Navier-Stokes equations.Because the tubular walls are assumed to be elastic, when stretched or compressed they exert forces on the fluid. Since these forces are singularlysupported along the boundaries, the fluid velocity and pressure fields become unsmooth. To accuratelycompute the solution, we use the velocity decomposition approach, according to which pressure and velocity are decomposed into a singular part and a remainder part.The singular part satisfies the Stokes equations with singular boundary forces.Because the Stokes solution is unsmooth, it is computed to second-order accuracyusing the immersed interface method, which incorporates known jump discontinuitiesin the solution and derivatives into the finite difference stencils.The remainder part, which satisfies the Navier-Stokes equations with a continuousbody force, is regular.The equations describing the remainder part are discretized in time usingthe semi-Lagrangian approach, and then solved usinga pressure-free projection method.Numerical results indicate that the computed overall solution is second-orderaccurate in space, and the velocity is second-order accurate in time. |
