Numerical Simulation of Unsteady Channel Flow with a Moving Indentation Using Solution Dependent Weighted Least Squares Based Gradients Calculations over Unstructured Mesh

Abstract

Fluid-structure interaction problem – unsteady channel flow with a moving indentation problem, which represents flow features of oscillating stenosis of a blood vessel, is numerically simulated here. The flow phenomenon inside the channel with a moving boundary is found to be unsteady and complex mainly due to the presence of the moving boundary and its interaction with flowing fluid. In this article, a high order accurate Harten–Lax and van Leer with contact for artificial compressibility Riemann solver has been used for flow computation. The Riemann solver is modified to incorporate arbitrarily Lagrangian–Eulerian (ALE) formulation 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) based gradient calculation. The present numerical scheme is validated here and the numerical results produced are found to agree with experimental as well as numerical results reported in the literature.