Kj. Badcock, A PARTIALLY IMPLICIT METHOD FOR SIMULATING VISCOUS AEROFOIL FLOWS, International journal for numerical methods in fluids, 19(3), 1994, pp. 259-268
A partially implicit method for the unsteady compressible Navier-Stoke
s equations is developed. The method is based on an explicit treatment
of streamwise fluxes and an implicit treatment of normal fluxes. This
leads to a linear system which is generated by an efficient finite di
fference procedure and which is block pentadiagonal. The method is tes
ted on a shock-induced oscillatory flow over an aerofoil. Parallel imp
lementations of an explicit, fully implicit and partially implicit met
hod are investigated.