Dynamic Deformation Of The Grid-based Unsteady Viscous Flow Numerical Analysis

In aircraft design, efficacious and accurate numerical simulation for steady or unsteady flow, especially for transonic flow is a crucial problem for designers. And the research of this dissertation is focused on how to efficaciously accurately simulate numerically the unsteady subsonic and transonic viscous flows.Solving the elliptic grid generation together with an algebraic method marching along the normal-to-wall direction, viscous grids around complex geometries are generated. By using TFI of displacements, we can get the unsteady viscous grid in any time. And the grid deformation process becomes completely independent of the generation of the initial grid; an important feature of the deforming grid procedure is that it must maintain the overall quality of the initial grid by introducing minimal distortion of the cells in the regions where the flow is likely to be changing rapidly. It is particularly important to keep the grid as rigid as possible in the near-wall regions and allow cell distortion towards the far-field, or at least in the regions of low gradients where the flow is not changing rapidly.The steady and unsteady viscous flow solvers based on Jameson's cell-centred finite volume method, and Jameson's dual method with Runge-Kutter scheme as inner iteration scheme have been development in this dissertation. In dual time method, there are real time and the pseudo-time, at each real time step marches the solution in a pseudo-time to steady state through an explicit time marching scheme, and the equation have two-order accuracy in time. We can make the solver more laconic and spend less time to get the numerical result. Baldwin-Lomax turbulence model is implemented in Navier-Stokes flow solver. In order to efficacious simulate the Navier-Stokes flow, some standard convergence acceleration techniques, such as local time stepping and implicit residual smoothing, and "ghost" cells which make complex boundary conditions simply have been used.To confirm the validity, effectivity and reliability of developed flow solvers, testcases of steady/unsteady subsonic and transonic flow of NACA0012, RAE2822, NACA64A010 airfoils. The result of flow field computation is good agreement with experiment; the method and the procedure presented in this paper are verified.