# Backward-facing Step in 2D

## Problem Description

^{2}The step height is S = 4.9 mm. A constant bulk velocity U

_{B}= 0.14 m/s is forced by a constant volume force chosen as F = 0.4 m/s

^{2}. The dynamic viscosity of the fluid is 1.456e

^{-5}kg/m/s, with a density of 1 kg/m

^{3}. With the hydraulic diameter D = 2*H

_{1}of the channel above the step the Reynolds-Number of the flow is Re = 100.

## Numerical Setup

Two particle resolutions are simulated, with a cutoff length r_{c°}=°0.2*S
for the coarser and r_{c°}=°0.1*S for the finer resolution. For the initial
particle configuration, the particles are distributed on a Cartesian grid. The walls
boundary conditions are imposed according to the methodology described by Adami et
al. ^{1}

## Results

^{2}

^{1}S. Adami, H. Hu and N. Adams, "A generalized wall boundary condition for smoothed particle hydrodynamics,"

*Journal of Computational Physics,*vol. 231, pp. 7057-7075, 2012.

^{2}R. Issa,

*Numerical assessment of smoothed particle hydrodynamics gridless method for incompressible flows and its extension to turbulent flows,*PhD Thesis: University of Manchester, 2005.

^{3}S. Adami, X. Hu and N. Adams, "A transport-velocity formulation for smoothed particle hydrodynamics,"

*Journal of Computational Physics,*vol. 241, pp. 292-307, 2013.