Numerical Simulation of Unsteady Channel Flow with a Moving Indentation

The FSI problem - unsteady channel flow with a moving indentation problem, which represents flow features of oscillating stenosis of a blood vessel, is numerically simulated. The flow inside the channel with moving boundary results in transient and complex flow phenomena mainly due to the interaction between the moving boundary and the flowing fluid. In this paper, an accurate Harten Lax and van Leer with contact for artificial compressibility Riemann solver have been used for flow computation. The Riemann solver is modified to incorporate Arbitrarily Lagrangian-Eulerian (ALE) formulation in order to take care of mesh movement in the computation, where radial basis function is used for dynamically moving the mesh. Higher order accuracy over unstructured meshes is achieved using quadratic solution reconstruction based on solution dependent weighted least squares (SDWLS). The present numerical scheme is validated here and the numerical results are found to agree with experimental results reported in literature.

AN ANALYTICAL AND NUMERICAL STUDY OF UNSTEADY CHANNEL FLOW WITH SLIP

A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.