A Fully Coupled Navier-Stokes Solver for Fluid Flow at All Speeds

This article deals with the formulation and testing of a newly developed, fully coupled, pressure-based algorithm for the solution of fluid flow at all speeds. The new algorithm is an extension into compressible flows of a fully coupled algorithm developed by the authors for laminar incompressible flows. The implicit velocity–pressure–density coupling is resolved by deriving a pressure equation following a procedure similar to a segregated SIMPLE algorithm using the Rhie-Chow interpolation technique. The coefficients of the momentum and continuity equations are assembled into one matrix and solved simultaneously, with their convergence accelerated via an algebraic multigrid method. The performance of the coupled solver is assessed by solving a number of two-dimensional problems in the subsonic, transsonic, supersonic, and hypersonic regimes over several grid systems of increasing sizes. For a desired level of convergence, results for each problem are presented in the form of convergence history plots, tabulated values of the maximum number of required iterations, the total CPU time, and the CPU time per control volume.