Development of a Multidimensional Residual Distribution Solver for Large Eddy Simulation of Industrial Turbulent Flows

Sammanfattning: This thesis presents the results of the author's research activity to develop a time-space accurate flow-solver for Large Eddy Simulations (LES), based on the Multidimensional Residual Distribution approach. The aim of this work is the attempt to develop a compact high-order algorithm which includes multidimensional flow physics, in hope of creating a better algorithm for LES of turbulent compressible flows. The author proposes a natural extension of the multidimensional residual distribution (RD) schemes from steady-state computations, where these schemes have shown increased accuracy with reduced stencil and ease of parallelization, to unsteady computations by using Jameson's dual time steps approach. Thus the unstationary problem is reduced to the problem of finding a pseudo steady-state solution at each real-time step by using an efficient marching algorithm in pseudo-time. Second order accuracy both in space and in time can be obtained by using this approach. Firstly, we study the unsteady one dimensional Burgers equation, the two dimensional linear wave equation and the circular advection of the cone. Secondly, the multidimensional residual distribution discretization of the different terms of the Navier-Stokes equations is described. Proper boundary conditions are discussed. A series of test-cases are presented to assess the accuracy of the algorithm, as it has been implemented in our Navier-Stokes solver, called NAS3D. A new compact high-order discretization for the convective part of the Navier-Stokes equations is proposed. This scheme is proved to be of third order accuracy while having the same compact stencil as the second-order multidimensional residual distribution schemes. Details of three Sub-grid Scale (SGS) models for LES which have been implemented in our code are given. The parallelized code, which uses either MPI or PVM for message passing, proves to scale extremely well with the number of processors. Finally, some results from our LES simulations, both for a simple test-case, e.g. the LES of turbulent channel flow, and for some industrial applications are presented.