Abstract
This chapter describes the mathematical formulation for the 3D unsteady preconditioned compressible viscous flow solver developed by our research group. The finite-volume Navier–Stokes solver employs a high-resolution Roe’s scheme on unstructured grids. The unsteady flow is calculated with a matrix-free, implicit, dual-time-stepping scheme. A five-stage Runge–Kutta time-integration algorithm is used between each physical time-step to iterate the numerical solution in pseudo time until convergence is reached. The methods used to accelerate the convergence rate to steady state in pseudo time, which are local time-stepping and implicit residual smoothing, are briefly described. The characteristics-based boundary treatments are also discussed in detail.
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