An Efficient Hybrid WCNS-CPR Algorithm in Shock Capturing

An efficient hybrid shock-capturing algorithm based on WCNS (Weighted compact nonlinear scheme) and CPR (Correction procedure via reconstruction) is proposed. TVB (Total Variation Bounded) shock detection indicator is used to identify cells with shocks. Then WCNS is used to capture shocks in these cells, while other cells are calculated by CPR. A strategy of algorithm switching is developed. Numerical experiments are simulated to test accuracy, shock-capturing ability and computational efficiency. The results show that this hybrid algorithm achieves expected high-order accuracy and high resolution and has less computational cost compared to WCNS.