Density-based algorithms that employ low-Mach number preconditioning techniques to eliminate numerical sti¤ness and improve accuracy of low speed ‡ow regimes may sometimes experience slow convergence and increased di¢ culty to establish the …nal mass ‡ow. This is especially true for complex ‡ow situations, where the presence of a widely disparate range of ‡ow speeds and highly non-linear physics can impair the e¢ ciency of the iterative algorithm. The cause of such decreases in convergence rate of the numerical solution can be traced back to the modi…ed pressure wave speeds arising in the preconditioned equation system. In this work we propose a novel accelerator for density-based, time-marching algorithms to alleviate the numerical problems mentioned above. The technique employs intermittent updates to pressure based on the solution of an elliptic pressure-correction equation derived from continuity, with associated velocity corrections formulated consistently from the linearization of the coupled equations. Introducing additional pressure and velocity corrections in this manner signi…cantly improves both the local and global mass balance, as well as the overall convergence behavior of the algorithm.Numerical examples are presented to demonstrate the performance of a coupled, density-based solver combined with a continuity based convergence acceleration for a few representative complex ‡ow applications.
Nomenclaturep static ‡uid pressure, N m 2 v ‡uid velocity vector, m s T static ‡uid temperature, K ‡uid density, Kg m 3 E ‡uid total energy, E = C v T + v:v 2 , J Kg H ‡uid total enthalpy, H = E + p= , J Kg pseudo-time, s pseudo-time interval, s ! x coordinate vector, m ! dx coordinate vector displacement, m ! A surface area vector, m 2 V volume, m 3 .
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