Per Carlbom

Stability and non-normality of the k —e equations

Abstract The analytical and numerical solutions of the equations of the k-e turbulence model are analyzed. Under certain conditions on the boundary values and the interior values of k and e the analytical and numerical solutions are bounded. If the steady state solution is obtained numerically by a Runge-Kutta time-stepping method, then severe constraints on the time-step and the non-normality of the jacobian matrix make the convergence very slow. The simplifications and conclusions are supported by data from a numerical solution of flow over a flat plate.