Construction and application research of HLL-HLLC scheme

HLLC is one kind of schemes which resolve shock, contact, and rarefaction waves exactly and has high value of application in compressible fluid simulation. HLL scheme cannot deal with the contact and shear waves accurately, thus it has much more dissipation compared with the HLLC scheme. However, numerical tests have illustrated that HLLC scheme may suffer from shock instability phenomena in the vicinity of strong shock waves while it performs well in low speed and subsonic flow. HLL-HLLC scheme which is suitable for a larger range of flow is proposed through mathematical analyses of HLLC and HLL scheme. The new proposed scheme indicates the property of HLLC which has low order dissipation in low speed flow and can overcome the shortcoming of shock instability phenomena in high speed flow. The effectiveness and robustness of the proposed scheme free from shock instability phenomena is demonstrated through three numerical simulations: hypersonic flow on double wedge configuration, supersonic flow over backward-facing step and hypersonic flow over blunt body.