Licentiate seminar

A high order method for simulation of fluid flow in complex geometries

Defendant Main Advisor Extra Advisor Date
Erik Stålberg Dan Henningson Arne Johansson 2005-05-24

Martin Berggren, Tdb, Uppsala

Evaluation committee


A numerical high order difference method is developed for solution of the incompressible Navier-Stokes equations. The solution is determined on a staggered curvilinear grid in two dimensions and by a Fourier expansion in the third dimension. The description in curvilinear body-fitted coordinates is obtained by an orthogonal mapping of the equations to a rectangular grid where space derivatives are determined by compact fourth order approximations. The time derivative is discretized with a second order backward difference method in a semi-implicit scheme, where the non-linear terms are linearly extrapolated with second order accuracy. An approximate block factorization technique is used in an iterative scheme to solve the large linear system resulting from the discretization in each time step. The solver algorithm consists of a combination of outer and inner iterations. An outer iteration step involves the solution of two sub-systems, one for prediction of the velocities and one for solution of the pressure. No boundary conditions for the intermediate variables in the splitting are needed and second order time accurate pressure solutions can be obtained. The method has experimentally been validated in earlier studies. Here it is validated for flow past circular cylinder as an example of a physical test case and the fourth order method is shown to be efficient in terms of number of grid points. A new iterative solution method for prediction of velocities allows for larger time steps due to less restrictive convergence constraints. Descriptors: Navier-Stokes equations, compact high order difference methods, approximate factorization, curvilinear staggered grids, spectral methods, boundary conditions.
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