A new flux calculating method based on the original HLLC (Harten-Lax-Vanleer contact wave) approximate riemann solver for ideal magnetohydrodynamics (MHD) equations was developed. The governing equations were discretized by finite volume method

and the time integration employed the implicit LU-SGS (lower-upper symmetric Gauss-Seidel) scheme. A hyperbolic divergence cleaning technique was introduced to suppress divergence of magnetic field. The numerical results of 1-D MHD shock-tube problem showed that HLLC-MHD scheme could accurately capture the magnetohydrodynamics waves

and the maximum numerical error was not more than 10%. The results of 2-D Rotor problem showed that HLLC-MHD scheme could be used to simulate the multi-dimension ideal MHD problem and accurately capture the Alfven wave of magnetic field. By comparing the results with and without divergence cleaning technique

the hyperbolic divergence cleaning technique could drop the peak value of magnetic field divergence from 50 to 2

and restrain the magnetic field divergence accumulation in the high divergence region

but also propagate the error to the low divergence region and cause the accumulation of the divergence at the boundary. It will influence the stability of the calculation.