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978-3-8439-3097-0, Reihe Ingenieurwissenschaften

Michael Wurst Development of a high-order Discontinuous Galerkin CFD solver for moving bodies

151 Seiten, Dissertation Universität Stuttgart (2017), Hardcover, A5

In this work, a CFD solver was developed, where the spatial discretisation of the terms in the Navier-Stokes equations was carried out with the Discontinuous Galerkin (DG) method. It is a high-order method, which combines features of the Finite Volume Method (FVM) and the Finite Element Method (FEM). As it is typical in FEM, the vector of the conservative variables is represented by a polynomial inside a cell. The order of the polynomial determines the order of the scheme. As jumps in the solution between individual cells are possible, a numerical Riemann solver, which is often used in FVM schemes, is needed for the definition of a unique flux between these cells.

The now developed CFD solver is especially eligible for the simulation of flow bodies which move relatively to the main flow direction. As the solver should be used for industrial applications, which are characterised by a high Reynolds number, the basis for the discretisation are the Reynolds-Averaged Navier-Stokes (RANS) equations. For the closure of the RANS equations the Spalart-Allmaras (SA) model was implemented as turbulence model. With these prerequisites, in a first step a solver for steady problems was developed and validated.

The main topic of the work are methods for moving bodies. Two methods are presented and implemented in the solver: the Arbitrary Lagrangian Eulerian (ALE) method and Chimera grids. The ALE method can be used for small movements of the body, as its movement results in a deformation of the grid, which may lead to non-valid cells for large deformations. In the ALE methods, a reference configuration exists for the grid points, which makes it possible to switch between a fixed Euler frame and a material Lagrange frame or chose a configuration in between, respectively. The here implemented method is freestream preserving and does not reduce the order of the method. The deformation of the grid is carried out with Radial Basis Functions (RBF), which guarantee valid cells.