Improvements in Flux-Difference Splitting Algorithm for Accurate and Robust Flow Simulations

Abstract

Conservative Supra-Characteristics Method (CSCM), a variant of Roe’s flux-difference splitting formulation, was developed formerly as a viable engineering prediction tool for aerodynamic design and had indeed shown its versatility in computing such complex flows as hypersonic/supersonic jet interaction field. The method adopted the characteristic boundary conditions implicitly at the boundary by identifying five characteristics embedded in the governing equations. But the lack of consistency in formulation as well as its complexity deterred it to be a popular algorithm for widespread use. In an effort to retain the characteristic boundary procedure associated with CSCM, a flux-difference formulation has been devised that follows Roe’s linearization but formulates like CSCM, decomposing the conservative Jacobian matrix into product of transformation matrices. The latter enables one to recognize that the governing conservative equations are indeed another form of characteristic equations, thereby clarifying the use of characteristics at the boundary. The validity of current numerical method is demonstrated for wide range of flows. Accuracy of solutions is enhanced through second-order extension in space, and shock instability is overcome for 2-D flow as well as 3-D flow. Robustness of numerics is proven by capturing unsteady nature of jet impingement through modification of dissipation terms in the Roe flux. With proper inflow conditions, both mass flow rate and total pressure are also shown to be conserved for a nozzle flow.