Abstract
AbstractAlgorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient‐based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier‐Stokes equations on a structured grid. The algorithm and software are based on the robust two‐level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two‐level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well‐known 3D lid‐driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE‐type preconditioner.
Highlights
The incompressible Navier-Stokes equations accurately describe flow of Newtonian fluids like water and air at low Mach numbers
We presented a robust method for solving the steady, incompressible Navier-Stokes equations, which makes use of parallelepiped shaped overlapping subdomains
On the interfaces of the subdomains, Householder transformations are applied to decouple all but one velocity node from the pressure nodes, after which all decoupled nodes can be eliminated in parallel
Summary
The incompressible Navier-Stokes equations accurately describe flow of Newtonian fluids like water and air at low Mach numbers. The discretization we use does not introduce artificial diffusion and is popular for direct numerical simulations of turbulent flow. In this flow regime, one is typically interested in accurately resolving the temporal evolution of the flow. The relatively small time steps in such a simulation allow simplifications in the solution process, in particular, Picard linearization (instead of Newton’s), and a segregated solution scheme that treats the velocities and pressure separately.[1]. On the other end of the spectrum are Stokes flows and flows at very low Reynolds numbers. This class of linear solvers tries to reduce the problem to scalar linear systems that can be solved by multigrid methods
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