A comparative study of TV stable schemes for shock interacting flows

  • Takayuki Aki
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 323)


New TV stable schemes for solving the Euler equations of compressible flow were applied to compute time-dependent shock interacting flows. Results obtained showed that the schemes tested will equally applicable to muti-dimensional shock interacting flows under a generalized coordinate framework as the TVD schemes were the case, though within the second order accuracy. The present results showed that key features of shock dynamics will be captured by using any scheme tested. However, extended use of the TVB scheme at further higher order might be criticized due to its accuracy correcting method using the differences tencil symmetrically fixed, which result mostly source of oscillation in the solution due to recovery of unlimited numerical flux as was in classical difference schemes. Merit of using the UNO scheme will be realizable at some higher order accuracy than the second one or by possible improvements of the present numerical flux function to ones upwind biased at the second order. Because the UNO scheme at higher order requires more computational effort compared to its second order one, study upcoming shall be directed to this. Considering the existing TVD schemes, even at higher order, can produce an efficient code for vector computers available today. They will continue to preserve their superiority in the sense stated above until a higher order upwind biased UNO scheme with efficiency competitive with the TVD ones can be available in future study.


Slip Surface Order Accuracy Numerical Flux High Order Accuracy Shock Interact 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Yee,H.C. et al., NASA TM100097, 1988.Google Scholar
  2. [2]
    Harten,A., JCP. Vol. 71, 1987.Google Scholar
  3. [3]
    Yee,H.C., NASA TM8946, 1987.Google Scholar
  4. [4]
    Shu,C.-W., Math. Comp. Vol. 49, 1987.Google Scholar
  5. [5]
    Harten,A. and Osher,S., SINUM. Vol. 24, 1987.Google Scholar
  6. [6]
    Roe,P., Lectures in Applied Mathematics, Vol. 22-Part 1, 1985.Google Scholar
  7. [7]
    Aki.T., Lecture Notes in Physics, Vol. 264, 1986.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Takayuki Aki
    • 1
  1. 1.National Aerospace LaboratoryChofu, TokyoJapan

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