A hybrid flux splitting method for compressible flow

ABSTRACT

A hybrid flux splitting scheme, called AUSM⁺–FVS((advection upstream splitting method)⁺–flux vector splitting), is proposed in this article to calculate the inviscid fluxes of Euler/Navier–Stokes equations. This new scheme is obtained by hybridizing the AUSM+ scheme with FVS method. When the local Mach number tends to zero, this scheme is similar to the AUSM+. Contrarily, this scheme is similar to the FVS at the shock region. Thus, this scheme has the accuracy of AUSM+ in boundary layer region and the robustness of FVS in shock region. Several numerical tests show that AUSM⁺–FVS can reduce the shock instability and has a good accuracy in boundary layer region.

Nomenclature

a	=	acoustic speed, m/s
e	=	total energy, J/kg
H	=	enthalpy, J/kg
M	=	Mach number
p	=	pressure, Pa
q	=	heat flux, W/m2
T	=	temperature, K
u	=	velocity in x-direction, m/s
v	=	velocity in y-direction, m/s
w	=	velocity in z-direction, m/s
x	=	Cartesian coordinate, m
y	=	Cartesian coordinate, m
γ	=	specific heat ratio
λ	=	thermal conductivity, Wm−1K−1
μ	=	dynamic viscosity, Pa s
ρ	=	density, kg/m3
τ	=	time, s

Subscripts
f	=	fluid
w	=	wall
	=	freestream

Nomenclature

a	=	acoustic speed, m/s
e	=	total energy, J/kg
H	=	enthalpy, J/kg
M	=	Mach number
p	=	pressure, Pa
q	=	heat flux, W/m2
T	=	temperature, K
u	=	velocity in x-direction, m/s
v	=	velocity in y-direction, m/s
w	=	velocity in z-direction, m/s
x	=	Cartesian coordinate, m
y	=	Cartesian coordinate, m
γ	=	specific heat ratio
λ	=	thermal conductivity, Wm−1K−1
μ	=	dynamic viscosity, Pa s
ρ	=	density, kg/m3
τ	=	time, s

Subscripts
f	=	fluid
w	=	wall
	=	freestream

Additional information

Funding

The present work was supported by the Key Project of International Joint Research of NSFC (51320105004) and the 111 Project (B16038).