LAUSR

Funding information NSAF, Grant/Award Number: U1530145; NKRDPC, Grant/Award Number: 2016YFA0401200; SCP, Grant/Award Number: TZ2016002; NSFC, Grant/Award Number: 11872067 and 91852203 Summary Many efforts have been made to improve the accuracy of the conventional weighted essentially nonoscillatory (WENO) scheme at transition points (connecting a smooth region and a discontinuity point). This paper analyzes these works and further develops a more effective multistep WENO scheme. Theoretical analysis and numerical results show that the new scheme not only improves the accuracy by one order higher than the traditional fifth-order WENO schemes at transition point but also maintains the fifth-order accuracy in smooth regions even at critical point where the first derivative vanishes.