HLL-HLLC格式的构造与应用研究

Construction and application research of HLL-HLLC scheme

HLLC格式是一种单调高分辨率格式,能够精确捕捉激波、接触间断和稀疏波,在可压缩流动中具有很高的应用价值;HLL格式相较于HLLC格式,抹平了接触间断,具有较大的数值耗散。然而,数值计算表明,在低马赫数和跨声速计算中表现较好的HLLC格式,在高马赫数强激波附近出现了激波不稳定现象。本文意图通过研究HLLC和HLL格式的数学性质,构造出一种适合更大马赫数范围的HLL-HLLC格式。新格式在较低马赫数下表现出HLLC的性质,是一种低耗散的格式;在高马赫数时具有HLL格式的性质,能够克服激波不稳定现象。通过对高超声速双楔流动、超声速后台阶流动和高超声速钝头体流动数值模拟证明了本文构造格式克服激波不稳定现象的有效性和鲁棒性。

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.