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Abstract
A large variety of practical problems in fluid dynamics requests an intimate coupling of the computational domain, the grid and the physical characteristics of the flow field. In the present research moving and adaptive grids are used for the prediction of three dimensional compressible flows, in steady or unsteady regime.
The research follows two main objectives. First, we propose a robust method for the prediction of fluid flows, applicable for complex geometries, with moving boundaries. This method correctly represents the particular conditions related to moving meshes. Secondly, a new grid adaptivity technique has been developed. The technique is based on the error analysis and consists in moving the grid points according to an uniform error distribution in the computational domain.
The Euler equations, obtained directly from the Navier-Stokes equations neglecting the viscous dissipation terms, are used to predict inviscid, compressible and rotational flows. The computation method is based on a finite volume technique of first order in space and an implicit or explicit time discretisation. The implicit method allows greater time steps, but request additional computer resources.
Tetrahedrons are used as discretisation elements and the flow variables are constants over each elementary cell. If the flow field boundaries are moving, the grid points will follow their evolution in time. The displacement of the grid satisfies the Geometric Conservation Laws (GCL) and is intimately related to the flow solver. The numerical modeling of those laws for three dimensional flow solvers on moving grids represents a premiere.
An Euler-Lagrange formulation, applied for moving control volumes, has been used to solve the flow equations, written in their conservative integral form. The flux at the interface of two adjacent cells is computed using the approximate Roe solution to the Riemann problem. This scheme implicitly satisfies the Rankine-Hugoniot jump conditions across a shock wave and does not require additional artificial viscosity.
The proposed methods have been applied for three dimensional internal and external flows on static and moving grids. The explicit and implicit time discretisation techniques have been validated for three dimensional internal flows with shock interactions. Other simulations are also presented: the flow around a transonic ONERA M6 wing, the flow inside a transition duct with complex geometry and inside a cylinder with incidence. The unsteady flow inside a shock tube is predicted by using the explicit and implicit method. Rectangular geometries with moving walls have been used for the validation of the numerical solution of flows on moving grids.
The adaption procedures are tested and validated for two dimensional situations. The results of some simulations made for subsonic compressible flows and for flows with discontinuities as shock waves are presented. Comparisons are made between the moving nodes adaptive method and the techniques based on grid reffinement and coarsening. Finally, the new adaptive grid technique has been used to study the transonic flow inside a channel and around NACA 0012 airfoil. (Abstract shortened by UMI.)