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On physics-based preconditioning of the Navier-Stokes equations. (English) Zbl 1395.65028
Summary: We develop a fully implicit scheme for the Navier-Stokes equations, in conservative form, for low to intermediate Mach number flows. Simulations in this range of flow regime produce stiff wave systems in which slow dynamical (advective) modes coexist with fast acoustic modes. Viscous and thermal diffusion effects in refined boundary layers can also produce stiffness. Implicit schemes allow one to step over the fast wave phenomena (or unresolved viscous time scales), while resolving advective time scales. In this study we employ the Jacobian-free Newton-Krylov (JFNK) method and develop a new physics-based preconditioner. To aid in overcoming numerical stiffness caused by the disparity between acoustic and advective modes, the governing equations are transformed into the primitive-variable form in a preconditioning step. The physics-based preconditioning incorporates traditional semi-implicit and physics-based splitting approaches without a loss of consistency between the original and preconditioned systems. The resulting algorithm is capable of solving low-speed natural circulation problems (\(M \sim 10^{-4}\)) with significant heat flux as well as intermediate speed (\(M\sim 1\)) flows efficiently by following dynamical (advective) time scales of the problem.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
35Q30 Navier-Stokes equations
Full Text: DOI
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