Newton-Krylov Algorithm with a Loosely Coupled Turbulence Model for Aerodynamic Flows

Abstract

A fast Newton-Krylov algorithm is presented that solves the turbulent Navier-Stokes equations on unstructured 2-D grids. The model of Spalart and Allmaras provides the turbulent viscosity and is loosely coupled to the mean-flow equations. It is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact Newton algorithm. We demonstrate that a loosely coupled algorithm is effective and has some advantages, such as reduced storage requirements and smoother transient oscillations. A transonic single-element case converges to 1 10 12 in 90 s on recent commodity hardware, whereas the lift coefficient is converged to three figures in one quarter of that time.

Multilevel Variable-Block Schur-Complement-Based Preconditioning for the Implicit Solution of the Reynolds- Averaged Navier-Stokes Equations Using Unstructured Grids

“…However, due to the uncoupling between the mean flow and the turbulent transport equations, the tandem solution strategy never yields quadratic convergence nor it is always able to drive the nodal residual to machine zero. The last statement cannot be generalized, since Blanco and Zingg [16,20] report convergence to machine zero for their loosely coupled approach on two-dimensional unstructured grids. However, even if convergence to machine zero is difficult to achieve, the nodal residual is always sufficiently converged for any practical "engineering" purpose and close enough to "true" steady-state solution to be a good initial guess for Newton's method.…”

“…Blanco and Zingg [18] adopt a similar strategy, but keep iterating the turbulence transport equation until its residual has become lower than that of the mean flow equations. The loosely coupled solution strategy is a choice often made as it "allows for the easy interchange of new turbulence models" [19] and also reduces the storage [18], compared to a fully coupled approach. However, due to the uncoupling between the mean flow and the turbulent transport equations, the tandem solution strategy never yields quadratic convergence nor it is always able to drive the nodal residual to machine zero.…”

“…In the early stages of the iterative process, the turbulent transport equation and the mean flow equations are solved in tandem (or in a loosely coupled manner, following the nomenclature used by Zingg et al [16]): the mean flow solution is advanced over a single pseudo-time step using an analytically computed, but approximate Jacobian while keeping turbulent viscosity frozen, then the turbulent variable is advanced over one or more pseudo-time steps using a FD Jacobian with frozen mean flow variables. Due to the uncoupling between the mean flow and turbulent transport equations, this procedure will eventually converge to steady state, but never yields quadratic convergence.…”

Computational fluid dynamics simulation of cryogenic safety analysis in an liquefied natural gas powered ship during liquefied natural gas leakage

“…Thus, the safety design analysis for LNG-powered ships is necessary, preferably in the basic design stage (Paik et al, 2011). Many researchers have developed the safety analysis simulation of LNG leakage hazards and established several models, such as zone models, integral models (Puttock, 1987;Shekhar et al, 2018), semiempirical models (Zhou et al, 2013), and computational fluid dynamics (CFD) models (Pula et al, 2005;Blanco and Zingg, 2007;Luketa-Hanlin et al, 2007). Among them, CFD simulation has been widely applied to analyze the leakage risk of LNG-powered ships under various conditions such as cryogenic impact, gas diffusion and explosion progress (Rigas and Sklavounos, 2006;Gavelli et al, 2008).…”