Numerical Simulation of Compressible Viscous Flow using a Velocity-Pressure-Vorticity Variational Formulation and Direct Solver

摘要

The two-dimensional Navier-Stokes equations for compressible viscous flow are solved by iterating on the kinematics, pressure, momentum and temperature equations producing a solution that satisfies continuity and vorticity definitions up to machine accuracy. Given a vorticity and mass fields, a functional is constructed to measure the kinematic imbalance of a velocity field. The velocity equations are produced by minimizing a discrete functional, subject to constrains imposed by boundary conditions. A suitable preconditioning and interpolation technique are used to balance precision and computation speed. The Poisson equation for pressure is solved similarly by minimizing a suitable functional. The momentum and energy equations are solved using a finite volume approach. A controlled amount of artificial viscosity and diffusion is respectively added according to mesh size and Reynolds number, resulting in a stable calculation via a direct solver.