Large-scale stabilized FE computational analysis of nonlinear steady-state transport/reaction systems

• Published in: Computer methods in applied mechanics and engineering Vol. 195; no. 13-16; pp. 1846 - 1871
• Main Authors: Shadid, J.N., Salinger, A.G., Pawlowski, R.P., Lin, P.T., Hennigan, G.L., Tuminaro, R.S., Lehoucq, R.B.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.02.2006; Elsevier
• Subjects: Bifurcation; Computational techniques; Continuation; Domain decomposition; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Mathematical methods in physics; Multilevel; Newton-Krylov; Parallel; Physics; Stability analysis; Stabilized finite elements; Steady-state; Transport-reaction; Stabilized finite elements; Transport-reaction; Continuation; Newton-Krylov; Multilevel; Bifurcation; Stability analysis; Parallel; Steady-state; Domain decomposition; Predictor-corrector methods; Heat equation; Complex system; Finite element method; Linear stability; Modelling; Transport equation; Non equilibrium system; Chemical reactions; Continuation method; Steady state; Mass transfer; Subsonic flow; Motion transfer; Heat mass transfer; Algebraic equation; Transport processes; Non linear effect; Navier-Stokes equations; Analytical continuation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2005.05.047

The solution of the governing steady transport equations for momentum, heat and mass transfer in fluids undergoing non-equilibrium chemical reactions can be extremely challenging. The difficulties arise from both the complexity of the nonlinear solution behavior as well as the nonlinear, coupled, non-symmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this paper, we briefly review progress on developing a stabilized finite element (FE) capability for numerical solution of these challenging problems. The discussion considers the stabilized FE formulation for the low Mach number Navier–Stokes equations with heat and mass transport with non-equilibrium chemical reactions, and the solution methods necessary for detailed analysis of these complex systems. The solution algorithms include robust nonlinear and linear solution schemes, parameter continuation methods, and linear stability analysis techniques. Our discussion considers computational efficiency, scalability, and some implementation issues of the solution methods. Computational results are presented for a CFD benchmark problem as well as for a number of large-scale, 2D and 3D, engineering transport/reaction applications.