A fully implicit low Mach number algorithm for flows with heat transfer

A class of implicit algorithms are presented to solve the momentum, continuity and enthalpy equations simultaneously for low Mach number flows that are driven by heat transfer and buoyancy. An exact Newton linearization is pursued, and quadratic convergence is obtained for buoyantly unstable heated perfect gas flow, with and without system acceleration. The novelty of this work is an orders of magnitude acceleration in convergence rate compared to fully segregated and partially segregated schemes that invoke Picard linearization, which exhibit linear convergence characteristics. Elements of an algebraic multigrid strategy are developed to solve the block coupled system of equations that arise. Intergrid transfer operations are based on the additive correction method, and coarse grid agglomeration is performed with anisotropic coarsening. An Incomplete LU factorization is used for smoothing error on different grid levels. A variety of low Mach number flow problems with heat transfer are studied to demonstrate convergence performance of the scheme. Quadratic convergence and significant CPU time improvements are observed for all test cases.