Viscosity Variability Impact on 2D Laminar and Turbulent Poiseuille Velocity Profiles; Characteristic-Based Split (CBS) Stabilization

The erosion of riverbeds and riverbanks depends, among other causes, both on the velocity fields and on their gradient near their boundaries, with the generation of shear stresses. The presence of sediments modifies the viscosity and, accordingly, modifies the profiles, particularly near the edges right where they are generated. Therefore, in this work, the distortion of the velocity profiles due to an imposed spatial variability of viscosity, was studied applying the Computational Fluid Dynamics (CFD). In particular, as test cases, laminar and turbulent Plane Poiseuille flows, were selected. For simplicity, it was assumed that the sediment distribution and therefore the viscosity distribution was not influenced by the mixing due to velocity field. That is, the equilibrium configuration was determined as a consequence of a spatially variable distribution of viscosity. The 2D Navier-Stokes equations, in steady state conditions, were numerically solved exploiting a research software developed and discussed by the author [1]. The turbulence was considered through the RANS (Reynolds Averaged Navier Stokes) approach. The two equations k - ε models were employed. The turbulence phenomena near solid boundaries was simulated by the means of Wall-Functions. Spatial discretization was carried out using the Finite Element Method (FEM). A structured meshing with h like adaptability was developed. Then, in order to avoid velocities and pressure instabilities, the Characteristic-based split algorithm (CBS) was applied, while, in order to correctly consider incompressibility, by a numerical point of view, the Method of Artificial Compressibility (AC) was selected. Accordingly, the related CBS-AC three steps algorithm was implemented [1]. Then, some parametric numerical experiments were performed, considering a semi-implicit, approach. As was to be expected, the velocity profiles, for both laminar and turbulent were influenced by the viscosity distribution. The discussion of the overall results points out the sensitivity of the algorithms not only to the meshes size, to their distribution and to the number of iterations, but also to some intrinsic "experimental numerical dials" (safe coefficients, explicit vs implicit ratio), specific of the selected approach. Moreover, suggestions have emerged for more complex and more complete simulations which, necessarily, would use methods based on iterations internal to each time-step.