Contribution to the development of an adaptive solver for numerical simulation of steady and unsteady flows

摘要

The work deals with enhancing the capabilities of the unstructured adaptive Finite Volume flow solver QUADFLOW for compressible fluid flow. The solver exists as an integrated tool with multiscale based grid adaptation and B-spline based quadrilateral/hexahedral multi-block grid generation modules. Due to hanging nodes introduced through grid adaptation, data structure is cell face based. Upwind methods are implemented for flux discretisation in combination with explicit time integration as well as implicit temporal discretisation using Newton linearisation and Krylov subspace method. In the thesis, a preconditioner based on the formulation of Weiss and Smith is implemented for simulating inviscid and viscous flows at low Mach number over airfoils in cruise as well as high lift configurations. The results demonstrate the achievement of Mach number independent lift and drag coefficients (D'Alembert's paradox) and have an excellent agreement with results available in the literature. The wall distance for the turbulence modelling in the presence of highly stretched, refined cells and hanging nodes close to the wall is correctly estimated using vector algebra. With this formulation, the wriggles in the skin friction distribution due to grid adaptation are avoided. Detached Eddy formulation based on the Spalart-Allmaras turbulence model is shown to be effective together with the grid adaptation and demonstrated to have excellent stall capturing characteristics for high lift configurations. A second order accurate, geometrically conservative implicit scheme, based on Backward Difference discretisation is formulated, implemented and validated to simulate the unsteady inviscid flow over the pitching NACA0012 profile. The method shows an advantage over the existing Mid-point scheme allowing relatively higher time steps and higher global CFL numbers during the simulation. The non-linear multigrid method based on the Full Approximation Storage scheme with V-cycle is implemented to improve the convergence behaviour of the explicit scheme in solving inviscid flow problems. The coarsening is based on the hierarchical agglomeration strategy to combine the fine cells belonging to the identical parent cell at the same level to generate a series of coarse grid levels. The restriction operator is based on the volume weightiness and the prolongation operation is carried out using the upwind scheme. The implementations in the solver are extensively validated using results from available experiments and numerical solutions existing in the literature. Fully turbulent flow computations at different free stream Mach numbers and Reynolds numbers are carried out and compared with data obtained from the KRG experiments conducted in Goettingen on behalf of SFB 401, including some tests where strong shock-boundary layer interaction with buffet was observed. These are studied at three different grid resolutions. It is concluded that the adequate resolution of the grid cells along the stream-wise direction is vital in accurately resolving the flow physics in shock buffet. Furthermore, code extensions are carried out to offer the capability to the adaptive solver for simulating three-dimensional flow and some first computations are performed with the available computational power.