Licentiate seminar

Higher order methods suitable for direct numerical simulation of flows in complex geometries

Defendant Main Advisor Extra Advisor Date
Arnim Brüger Arne Johansson Dan Henningson 2002-06-14

Jakob Yström, NADA, KTH

Evaluation committee


A method was implemented aiming at direct numerical simulation (DNS) of turbulent flow problems. It allows handling of two-dimensional curvilinear grids with orthogonal transformations. The grid type is staggered in order to suppress parasitic pressure oscillations. Compact fourth order Pade operators are used for all space derivatives, partly as staggered and partly as regular type. The advantages of this discretization technique are a significantly smaller error constant in the truncation error and better dispersion behavior. On the other hand the implementation is more difficult. The Navier-Stokes equations are solved in primitive variables. The time derivative is discretized with the second order backward difference method, with explicitly treated nonlinear terms. Pressure terms and the divergence condition enter the implicit left hand side. An approximate factorization method was 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 was formulated in an iterative scheme. Also, the two arising subsystems are solved by iterative methods. Some effort was put in the validation of the method. A number of numerical experiments were carried out. Spatial convergence tests demonstrate that fourth order accurate solutions were obtained. Second order accurate solutions in time were achieved for the velocity components and the pressure. Performance tests were run for estimation of execution time and memory consumption in large simulations.