Higher-order in time "quasi-unconditionally stable" ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvil

This paper introduces alternating-direction implicit (ADI) solvers of higher order of timeaccuracy (orders two to six) for the compressible Navier-Stokes equations in two- and threedimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas-Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDFbased ADI algorithms proposed in this paper are “quasi-unconditionally stable” in the following sense: each algorithm is stable for all couples (h, ...

• Type: Journal
• Year: 2016
• Where: JCPHY
• Authors: Oscar P. Bruno, Max Cubillos
• Keywords: JCPHY 2016