Study. Ctvd Format Applications And Related Issues

The paper consists of three parts. In the first part, we present CTVD scheme as a Jacobian-free solver for ideal magnetohydrodynamics(MHD) equations which have complicated characteristics. CTVD scheme, as a second order-order scheme in space and time, avoids characteristic decomposition of the Jacobian and is efficient for MHD computations. After using local Lax-Friedrichs flux splitting instead of global Lax-Friedrichs flux splitting in Yu[25], we get more accurate numerical results in MHD computations. The results of several one-dimension and two-dimension tests demonstrate that CTVD scheme is an efficiency, and has high resolution in MHD computations.In the second part, we use high-resolution CTVD scheme to solve the Euler equations of multi-component flows. The numerical experiments of conservative CTVD scheme for the gas mixtures only produces slight oscillations near the interfaces. And the oscillations disappear when the computation is on very fine grids. We also adopt a non-oscillation TVD scheme(NOSl) to solve the non-conservative equations and the CTVD scheme eliminates the oscillations when being applied to the non-conservative equations.In the third part, we proposed two methods to cure the numerical shock instability for HLLC Riemann solver in two-dimension Euler equations. One method uses the rotated method and the other one is the hybrid method. Taking into account the efficiency, accuracy and robustness, the hybrid method is better than rotated method for HLLC solver. A series of test problems prove this conclusion.