A Taylor Weak Statement Finite Element Algorithm for Real-Gas Compressible Navier-Stokes Simulation

A new finite element numerical computational fluid dynamics (CFD) algorithm has been developed for efficiently solving multi-dimensional real-gas compressible flow problems in generalized coordinates on modern parallel-vector computer systems. The algorithm employs a Taylor extension on the classical Galerkin weak statement formulation, a time-relaxed iteration procedure, and a tensor matrix product based factorization of the linear algebra jacobian under a generalized coordinate transformation. Allowing for a general conservation law system, the algorithm has been exercised for the two-dimensional Euler and the laminar and turbulent forms of the Navier-Stokes equations. Equilibrium real-gas air properties are admitted, and numerical results verify solution accuracy, consistency, convergence, efficiency, and stability over a range of test problem parameters. The algorithm is cast in a fully generalized form, such that extension to other flow problems, including three dimensions or two-phase thermal-hydraulics, is direct.