Arbitrary Steady-State Solutions with the K-Epsilon Model

Widely used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size, which can occur even when attempting to use the K-epsilon model within its intended scope as a fully turbulent computation. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, use of a low-Reynolds-number damping term in the a equation causes the degenerate solution to act as a stable fixed point under certain conditions, in turn causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.