Solution-limited time stepping to enhance reliability in CFD applications

  • Authors:

  • Chenzhou Lian;Guoping Xia;Charles L. Merkle

  • Affiliations:

  • School of Mechanical Engineering, Purdue University, ARMS 3142, 701 W. Stadium Ave., West Lafayette, IN 47907-2045, United States;School of Mechanical Engineering, Purdue University, ARMS 3142, 701 W. Stadium Ave., West Lafayette, IN 47907-2045, United States;School of Mechanical Engineering, Purdue University, ARMS 3142, 701 W. Stadium Ave., West Lafayette, IN 47907-2045, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

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.