Internal Report

A hybrid high order method for incompressible flow in complex geometries / version 2

Author Document Type Year Download File size
Arnim Brüger, Erik Stålberg, Jonas Nilsson, Wendy Kress, Bertil Gustafsson, Per Lötstedt, Arne Johansson, Dan Henningson Technical report 2005 Not available
ISSN 0348-467X


A numerical method is presented for solution of the incompressible Navier-Stokes equations in primitive variables. The method can be applied to three dimensional, internal or external flows with one ore more periodic directions. Well posed formulations of the boundary conditions are used.The discretization is of hybrid type consisting of compact high order difference operators applied to a two dimensional curvilinear domain and a Fourier expansion in the periodic direction. Parasitic checkerboard oscillations in the pressure are suppressed by staggering the grid locations. Orthogonal transformations are used between computational and physical space. For stability reasons the local representation of velocities is chosen. The time derivative is discretized with the second order backward difference method in a semi-implicit scheme. An approximate factorization method is applied in order to solve the resulting large linear system of equations. It is based on a block LU factorization of an approximated system matrix. The solution procedure is formulated in an iterative scheme combining inner and outer iterations. The inner iterations consist of the solution of three subsystems, two for the velocities and one for the pressure.