Computational Fluid Dynamics: Science or Toolbox?

Over the past six decades the science of CFD has created a versatile computational toolbox. Still, enough barriers remain; for aeronautical CFD one of the highest ones is slow convergence to steady flow solutions. The importance of reducing method complexity to O(N) is discussed in the light of future massively parallel computing. In the same light a vision is outlined of CFD based on PDEs of the lowest possible order, i.e., the first order. Such a methodology will allow significant functional decomposition in addition to domain decomposition. To reap this benefit, a parallel architecture of distributed, sizable clusters of memory-sharing processors is recommended. Removal of computational barriers, and radical innovation will require increased fundamental research on algorithms, implying increased funding for such activity, and continued teaching of method development.