On the structure and use of linearized block implicit schemes

Numerical Uncertainties in Transonic Flow Calculations for Aerofoils With Blunt Trailing Edges

“…This region has been approximately modelled by a bubble closure profile when boundary layer approximations are used, but it is preferred to calculate its dimension by solution of the Navier-Stokes equations. 10 Computational procedures for transonic aerofoils are reviewed for example by Lock and Williams, 8 King and Williams, 11 and Cebeci et al 12 and can be divided into two categories: first, viscous-inviscid interaction methods 13 which solve either integral 8 or finite difference 14 boundary layer equations near the surface and either Euler 15,16 or potential flow 17,18 inviscid equations in the freestream; second, field methods which solve the compressible Navier-Stokes equations with a turbulence model in either finite difference [19][20][21] or finite element 22 form. Henne 5 calculated the transonic aerodynamics of DTE aerofoils by solving the inviscid Euler equations and integral boundary layer equations using the viscous-inviscid interaction procedure of Bauer et al 2 The choice of boundary layer equations forced Henne 5 to input two approximations: first, the shape of the recirculation in the wake was provided by empirically locating the streamline that divided forward and reverse flow in the wake of the divergent trailing edge; second, an experimental correlation was used to estimate base drag, since the code 2 does not calculate any variables, including pressure, in this region.…”

“…A well-established Reynolds-averaged Navier-Stokes 19,20 calculation procedure was chosen for the present contribution for the following reasons: the entire flow field can be calculated with a single set of equations; turbulence model approximations replace profile and streamline closure assumptions; effects of the wake and normal pressure gradient, which are needed in the vicinity of recirculation, are calculated; the matching of solutions to different equations at their boundaries is eliminated. Experience suggests that computational efficiencies promised by interactive methods might not be significant when compared with the present Navier-Stokes method in this complex aerofoil flow.…”

Solution of the Boltzmann Transport Equations for a Permeable Base Transistor.

“…The numerical method used in the solution of the governing equations, which were derived in the previous section, is based on an application of consistently split, linearized, block implicit (LBI) methods as developed by -Briley and McDonald [7,8]. …”

Numerical solution of the steady, compressible, Navier-Stokes equations in two and three dimensions by a coupled space-marching method

“…McDonald [29] were the first to develop implicit marching schemes using the altemating-direcdon-implicit (ADI) method for the multi-dimensional equations. The implicit formulation allows much larger time steps, and consequently steady-state convergence is generally reached much more rapidly.…”