TU Guo-hua, YUAN Xiang-jiang, XIA Zhi-qiang, HU Zhen. A Class of Compact Upwind TVD Difference Schemes[J]. Applied Mathematics and Mechanics, 2006, 27(6): 675-682.
Citation: TU Guo-hua, YUAN Xiang-jiang, XIA Zhi-qiang, HU Zhen. A Class of Compact Upwind TVD Difference Schemes[J]. Applied Mathematics and Mechanics, 2006, 27(6): 675-682.

A Class of Compact Upwind TVD Difference Schemes

  • Received Date: 2004-12-10
  • Rev Recd Date: 2006-02-25
  • Publish Date: 2006-06-15
  • A new method was proposed for constructing total variation diminishing(TVD)upwind schemes in conservation forms.Two limiters were used to prevent non-physical oscillations across discontinuity.Both limiters can ensure the nonlinear compact schemes TVD property.Two compact TVD(CTVD)schemes were tested,one is third-order accuracy,and the other is fifth-order.The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems,as well as a two-dimensional shock-vortex interaction and a shock-boundary flow interaction.Numerical results show their high-order accuracy and high resolution,and low oscillations across discontinuities.
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