Computations using the preconditioning BI-CGSTAB algorithm in chemical non-equilibrium problems

• Published in: International journal for numerical methods in fluids Vol. 28; no. 2; pp. 267 - 291
• Main Authors: Lin, Herng, Chieng, Ching-Chang
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 15.08.1998; Wiley
• Subjects: adaptive grid; Bi-CGSTAB method; Chemically reactive flows; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); non-equilibrium equations; Nonequilibrium gas dynamics; Physics; Reactive, radiative, or nonequilibrium flows; Computational fluid dynamics; Multicomponent mixture; Digital simulation; Hypersonic flow; Chemical reactions; Adaptive method; Gas mixtures; Algorithms; Non equilibrium flow; Reacting flow; Blunt body; Preconditioning; Numerical convergence; Mesh generation; Heat transfer; Concentration distribution
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19980815)28:2<267::AID-FLD712>3.0.CO;2-D

A robust method for solving the chemical non‐equilibrium Navier–Stokes equations, including all of the species conservation and energy production equations, is developed. The algorithm is embodied in a fully coupled, implicit, large block structure. Van Leer flux splitting for inviscid terms and central differencing for viscous terms in the explicit operators are applied in the numerical algorithm. The fully‐coupled system is solved implicitly and the bi‐conjugate gradient stable (Bi‐CGSTAB) method with a preconditioner of incomplete lower–upper (LU)‐factorization (ILU) is used for solving large block structure and diagonal dominate matrix equations. The computations are performed for the hypersonic inflow over blunt bodies including half cylinder, double ellipse and blunt nose. The adaptive grid constructed by moving grid method is employed to capture the shock location. Computational results in the present study are compared with other calculated data and exhibit good agreement. Convergence histories of the mean flow variables and species equations demonstrate that the fast convergent rate can be achieved by the preconditioned Bi‐CGSTAB method. © 1998 John Wiley & Sons, Ltd.