Solution-limited time stepping to enhance reliability in CFD applications

A method for enhancing the reliability of implicit computational algorithms and decreasing their sensitivity to initial conditions without adversely impacting their efficiency is investigated. Efficient convergence is maintained by specifying a large global Courant (CFL) number while reliability is improved by limiting the local CFL number such that the solution change in any cell is less than a specified tolerance. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. An upper limit on the local solution change is attained by a proper non-dimensionalization of variables in different flow regimes within a single problem or across different problems. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results such as negative densities, temperatures or species mass fractions during the computation. The method is tested against a series of problems all starting from quiescent initial conditions to identify its characteristics and to verify the approach. The results reveal a substantial improvement in convergence reliability of implicit CFD applications that enables computations starting from simple initial conditions without user intervention.