GUO Yan, LIU Ru-xun. Characteristic-Based Finite Volume Scheme for 1D Euler Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 291-300.
Citation: GUO Yan, LIU Ru-xun. Characteristic-Based Finite Volume Scheme for 1D Euler Equations[J]. Applied Mathematics and Mechanics, 2009, 30(3): 291-300.

Characteristic-Based Finite Volume Scheme for 1D Euler Equations

  • Received Date: 2008-07-04
  • Rev Recd Date: 2009-02-12
  • Publish Date: 2009-03-15
  • A highorder finitevolume scheme was presented for the onedimensional scalar and inviscid Euler conservation laws. The Simpson's quadrature rule was used to achieve highorder accuracy in time. To get the point value of the Simpson's quadrature, the characteristic theory was used to obtain the positions of the grid points at each sub-time stages along the characteristic curves, and the thirdorder and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction was adopted to estimate the cell point values. Several standard one-dimensional examples were used to verify highorder accuracy, convergence and capability of capturing shock.
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