Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
This paper develops a Newton-Krylov method for the solution of steady compressible Navier-Stokes equations by using a discontinuous Galerkin (DK) discretization on unstructured meshes. Steady-state solutions are obtained using Newton-Krylov approach, whereas the linear system at each iteration is solved by employing a restarted GMRES algorithm whose fast convergence is achieved by examining several different preconditioners. An element line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. The block-ILU(0) factorization is performed in-place, and a linearization is presented which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear \(p\)-multigrid preconditioner is considered, where block-Jacobi, line-Jacobi and block-ILU(0) are used as smoothers. This last preconditioner improves significantly convergence in terms of number of iterations and CPU time, compared to a single-level block-Jacobi or line-Jacobi preconditioner.
scientific article; zbMATH DE number 5566330
scientific article