Volume 32 Issue 2
Mar.  2012
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HOU Tianxiang, JI Zhen. Modified Two Dimensional Third-order Semi-discrete Central-upwind Scheme[J]. Journal of Space Science, 2012, 32(2): 197-203. doi: 10.11728/cjss2012.02.197
Citation: HOU Tianxiang, JI Zhen. Modified Two Dimensional Third-order Semi-discrete Central-upwind Scheme[J]. Journal of Space Science, 2012, 32(2): 197-203. doi: 10.11728/cjss2012.02.197

Modified Two Dimensional Third-order Semi-discrete Central-upwind Scheme

doi: 10.11728/cjss2012.02.197
  • Received Date: 2011-01-12
  • Rev Recd Date: 2011-11-17
  • Publish Date: 2012-03-15
  • The semi-discrete central-upwind scheme is a new Godunov type numerical method which is developed in 1990s. The scheme is widely used in the computational fluid dynamics and its advantages include the simple calculation process, the high calculation precision and so on. But for the third-order scheme, the positivity of the weight function and the non-oscillation of the WENO type reconstruction function in every direction cannot be preserved in two dimensional problems. In this article, a simple, direct modification is taken to the weight function of the two dimensional third-order semi-discrete central-upwind scheme. The modified weight function will keep the positivity all the time while the accuracy of the semi-discrete central-upwind method is preserved. The revised scheme still has the advantages of central-upwind schemes and it keeps the non-oscillation of reconstruction. To explore the potential capability of application of this reformation of weight function, two Magnetohydrodynamics (MHD) problems are simulated. In simulations, the third order Runge-Kutta method is used to solve the time evolution and the divergence of magnetic field was calculated by fourth-order Lax-Wendroff (L-W) scheme. All the numerical results demonstrate the modified scheme can solve the MHD equations stably, get high resolution and non-oscillatory results, keep the positivity of the weight function and the reconstruction is non-oscillatory in each direction.

     

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