High Resolution Finite Volume Schemes Based On CBC/TVD Conditions

The paper, based on CBC and TVD conditions, in the second chapter combined with QUICK scheme, constructs a new piecewise high-resolution finite volume numerical scheme (New QUICK scheme). Similarly, the third chapter, combined with Newton interpolation formula, constructs a new continuous high-resolution finite volume numerical scheme (NPUS). Two different numerical schemes are used to discrete convection terms. We find out that two solutions have high accuracy in a smooth region, and can be used to suppress unphysical oscillations and possess the boundedness and stability in the vicinity of steep gradients and discontinuities. But according to the numerical examples, the approximation effects of New QUICK scheme are not good at discontinuities. And the program of New QUICK scheme is complex. However NPUS easily program and has higher accuracy. High-resolution finite volume scheme usually adopt uniform grid to discrete convection term, because it is simple and easy to use. The two schemes adopt uniform Grids. However, Uniform Grid has a good effect on discrete convection with discontinuous initial value. So based on New QUICK scheme, the fourth chapter construct a new high resolution finite volume scheme under the non-uniform grid (QVSF). The numerical examples, compared to grid under two formats, demonstrate that high resolution finite volume in two different grids can better suppress non-physical shock, and uniform grid is more efficient to highlight the effect.