TRACE is a CFD (Computational Fluid Dynamics) tool, that solves the Unsteady Reynolds Averaged Navier Stokes Equations, known as URANS for the compressible flow, especially in the field of aerodynamics for tubomachinery. The Navier Stokes Equations describe the flow of gas in a continuum. In a three-dimensional space they consist of the continuity, three momentums and the energy equation. They are valid as long as the gas phase can be treated as a continuum, this means the density is high enough to approach the behaviour of the molecules statistically.

The Reynolds Averaging of the Navier Stokes Equation is made to consider the turbulent fluctuations of technical flows, which cannot be resolved today in technical flow due to the limited computing resources. This leads to an additional Tensor in the Navier Stokes Equations, the Reynold Stress Tensor. The problem is closed with the help of Turbulence Models, which describe the turbulent quantities of a flow and with the help of the Boussinesq Approximation the influence of turbulence is linked with the Stress Tensor of the Navier Stokes Equations via the turbulent Eddy Viscosity. In TRACE we use the k-omega Two-Equation Turbulence Model. Furthermore especially for turbomachinery TRACE has several extensions, e.g. non-reflecting boundary conditions, phase lag model, etc.

The URANS Equations in TRACE transformed into a rotating frame of reference and discretized in a Finite-Volume Framework. For the convection term a second order upwind scheme with MUSCL extrapolation is used, the Roe Flux-Difference Splitting Scheme. The diffusion terms are discretized using a second order central difference approach. The temporal discretization is an implicit backward Euler Scheme. The iterative solution towards the steady state or the periodic unsteady flow is done with a time matching algorithm. The system of equations are solved with a Symmetric Gauss-Seidel method or alternatively with a Predictor-Corrector algorithm using an ILU-Defactorization of the system matrix.