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

A numerical high order difference method is developed for solution of the incom-pressible 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 nonlinear 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 subsystems , 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 a circular cylinder as an example of a physical test case and the fourth order method is shown to be efficient in terms of grid resolution. The method is applied to external flow past a parabolic body and internal flow in an asymmetric diffuser in order to investigate the performance in two different curvilinear geometries and to give directions for future development of the method. It is concluded that the novel formulation of boundary conditions need further investigation. A new iterative solution method for prediction of velocities allows for larger time steps due to less restrictive convergence constraints. Preface This thesis considers the description and validation of an incompressible Navier-Stokes solution method. It is based on compact high order difference operators in two dimensions and a Fourier expansion in one dimension. This discretiza-tion allows for treatment of two dimensional curvilinear domains with a third periodic dimension. The thesis contains the following papers: A hybrid high order method for incompressible flow in complex geometries /version 2. TRITA-MEK 2005:06. 2005 Applications of a high order method for fluid flows in complex geometries. Internal report. Dan Henningson (DH) and Arne Johansson (AJ) formulated the goal and main strategy of a method designed for simulations of turbulent flow phenomena in complex geometries. The …