Self-Adaptive Newton-based iteration strategy for the LES of turbulent multi-scale flows

• Implicit time integration is studied in the context of compressible LES and DNS.
• Influence of condition number and convergence residual are assessed.
• A Self-Adaptive Newton (SAN) method is proposed to improve efficiency.
• Consistency with explicit time integration is checked.
• The SAN method is particulary efficient when mesh-size disparities are present.

An improvement of the efficiency of implicit schemes based on Newton-like methods for the simulation of turbulent flows by compressible LES or DNS is proposed. It hinges on a zonal Self-Adaptive Newton method (hereafter denoted SAN), capable of taking advantage of Newton convergence rate heterogeneities in multi-scale flow configurations due to a strong spatial variation of the mesh resolution, such as transitional or turbulent flows controlled by small actuators or passive devices. Thanks to a predictor of the local Newton convergence rate, SAN provides computational savings by allocating resources in regions where they are most needed. The consistency with explicit time integration and the efficiency of the method are checked in three test cases:–The standard test-case of 2-D linear advection of a vortex, on three different two-block grids.–Transition to 3-D turbulence on the lee-side of an airfoil at high angle of attack, which features a challenging laminar separation bubble with a turbulent reattachment.–A passively-controlled turbulent transonic cavity flow, for which the CPU time is reduced by a factor of 10 with respect to the baseline algorithm, illustrates the interest of the proposed algorithm.