Numerical-asymptotic expansion matching for computing a viscous flow around a sharp expansion corner
A new computational technique based on numerical-asymptotic expansion matching for describing the local singular behavior of a viscous flow around a sharp right-angle expansion corner is developed. The first two terms of asymptotic solution are used, and a matching with a time-marching finite difference scheme for Navier-Stokes equations is formulated. Local mesh refinements around the corner are required to meet the validity condition of the asymptotic solution. The presented numerical technique is applied to symmetric flow in a suddenly expanding channel with expansion ratio \(D/d = 3\) at various Reynolds numbers \(1\leq Re\leq 700\). The results are compared with those from a standard finite difference scheme that uses second-order forward/backward differences near the corner. It is found that the standard scheme results converge toward those of the present technique as the level of local refinement near the corner. These computations demonstrate that the use of local corner solution for numerical simulation of the flow in the channel enhances the accuracy of simulations and requires less computational effort (less refinements near the corners) to achieve the same converging numerical results.
scientific article; zbMATH DE number 1798881