Analysis of the energy exchange between atmosphere and ground using the compressible Navier-Stokes equations and the heat equation

In this paper the interface between the one dimensional compressible Navier-Stokes equation and the heat equation is analysed. For the linearized and symmetrized model, the energy method is used to derive interface conditions that bounds the solution. First, the characteristic far field boundary conditions are derived for the Navier-Stokes equation, second boundary conditions for a solid wall are derived and last interface condition with a heat equation. High order Summation-by-Parts operators are used for the spatial discretization. Boundary and interface conditions are weakly imposed using Simultaneous Approximation Terms. The implementation is stable and the method of manufactured solution is used to verify the implementation. An efficiency study showed that high order operators are superior in how much computer power is needed to get an accurate solution.