In this tutorial, the setup of a simulation of compressible Couette flow in a two-dimensional domain is demonstrated. This is a viscous, single-species problem. The following capabilities of HAMeRS will be shown:

• Fifth-order shock capturing method WCNS5-JS
• Sixth-order conservative and non-conservative viscous flux methods
• Fourth-order SSP-RK54 time integration method
• No-slip boundary conditions

Two parallel plates of infinite extent are separated by a distance h in the y-direction. Both plates are treated as no-slip isothermal walls at a temperature T_w. The top plate moves at a velocity U_w in the x-direction with respect to the bottom plate. In the case of ideal gas with constant ratio of specific heats γ, shear viscosity μ and thermal conductivity κ, there is an analytical solution for the Navier-Stokes equations:

Taking γ=1.4, μ=0.417 kg/(s·m), Pr=0.72, c_p=1005.0 J/(kg·K), h=1.0 m, T_w=300.0 K, U_w=69.445 m/s, we have p_c=1.0x10⁵ N/m², Ma=0.2 and Re=200.0.

The file containing the initial conditions of this problem (CouetteFlow2D.cpp) can be found in problems/Navier-Stokes and the initial conditions should be set up by ln -sf <absolute path to CouetteFlow2D.cpp> src/apps/Navier-Stokes/NavierStokesInitialConditions.cpp. The code has to be re-compiled after the link to the actual initial condition file is set.

The configurations of the input file are discussed in this section. The first thing to choose in the input file is whether it is an Euler (inviscid) or Navier-Stokes (diffusive and viscous) application. Since our problem is viscous, we first set the application type to be Navier-Stokes:

Application = "Navier-Stokes"