Preconditioners for hyperbolic systems are numerical artifacts to accelerate the convergence to a steady state.In addition, the preconditioner should also be included in the artificial viscosity or upwinding terms to improve the accuracy of the steady state solution. For time dependent problemswe use a dual time stepping approach. The preconditioner affects the convergence rate and the accuracy of the subiterations within each physical time step. We considertwo types of local preconditioners:Jacobi and low speed preconditioning.We can express the algorithm in several sets of variableswhile using only the conservation variables for the flux terms.We compare the effect of these various variable setson the efficiency and accuracy of the scheme.
