An approximate Roe-type Riemann solver for a class of realizable second order closures

International audienceA realizable, objective second-moment turbulence closure, allowing for an entropy carac-terisation, is analyzed with respect to its convective subset. The distinct characteristic wave system of these equations in non-conservation form is exposed. An approximate solution to the associated one-dimensional Riemann problem is constructed making use of approximate jump conditions obtained by assuming a linear path across shock waves. A numerical integration method based on a new approximate Riemann solver (ux-di erence-splitting) is proposed for use in conjunction with either unstructured or structured grids. Test calculations of quasi one-dimensional ow cases demonstrate the feasibility of the current technique even where Euler-based approaches fail