TU Guo-hua, YUAN Xiang-jiang, LU Li-peng. Developing Shock-Capturing Difference Methods[J]. Applied Mathematics and Mechanics, 2007, 28(4): 433-440.
Citation: TU Guo-hua, YUAN Xiang-jiang, LU Li-peng. Developing Shock-Capturing Difference Methods[J]. Applied Mathematics and Mechanics, 2007, 28(4): 433-440.

Developing Shock-Capturing Difference Methods

  • Received Date: 2006-02-24
  • Rev Recd Date: 2007-01-27
  • Publish Date: 2007-04-15
  • A new shock-capturing method was proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes were projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions were carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes were converted into conservative forms and the oscillation-free shock-capturing schemes were acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) were modified by the method for hyperbolic systems and the modified schemes were checked on several oneOdimensional and two-dimensional test cases. Some numerical solutions of the schemes were compared with those of a WENO scheme and an MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.
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