For several important classes of problems, the propagation behaviour inherent in the PDEs being solved can be exploited, leading to considerable savings in CPU requirements. Examples where this propagation behaviour can lead to faster algorithms include:

  • detonation: no change to the flowfield occurs ahead of the denotation wave;
  • supersonic flows: a change of the flowfield can only be influenced by upstream events, but never by downstream disturbances; and
  • scalar transport: a change of the transported variable can only occur in the downstream region, and only if a gradient in the transported variable or a source is present.

The present chapter shows how to combine physics and data structures to arrive at faster solutions. Heavy emphasis is placed on space-marching, where these techniques have reached considerable maturity. However, the concepts covered are generally applicable.

16.1. Space-marching

One of the most efficient ways of computing supersonic flowfields is via so-called space-marching techniques. These techniques make use of the fact that in a supersonic flowfield no information can travel upstream. Starting from the upstream boundary, the solution is obtained by marching in the downstream direction, obtaining the solution for the next downstream plane (for structured (Kutler (1973), Schiff and Steger (1979), Chakravarthy and Szema (1987), Matus and Bender (1990), Lawrence et al. (1991)) or semi-structured (McGrory et al. (1991), Soltani ...

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