High-order Numerical Flow Simulation Based On A Rotating Reference Frame

Being currently one of the most popular high-order methods in the field of computational fluid dynamics,the Discontinuous Galerkin Method possesses an excellent ability to describe flow-fields containing complicated vortices.Based on the high-order Discontinuous Galerkin Method and the noninertial rotating reference frame,research on the high fidelity numerical simulation of rotating flowfields is presented in this thesis.First of all,the governing Euler/Navier-Stokes equations and RANS equations coupled with a modified S-A turbulence model in the non-inertial rotating frame are derived and validated,along with the corresponding wall and far-field boundary conditions.The spatial discretization of the governing equations is then implemented using the high-order Discontinuous Galerkin Method.The famous Local Lax-Friedrichs scheme is adopted for the convective flux,while the BR2 scheme is employed for the viscous flux and the calculation of gradients.Meanwhile shock waves are captured within sub-grids through an artificial dissipation approach.In order to obtain more accurate expressions of the solid wall on the very coarse grid,the wall surfaces are approximated and reconstructed.An implicit time integration method and an implicit dual time-stepping method are adopted for the steady and unsteady temporal discretization,respectively.Whereas the huge linear system generated during the iterations is solved using either the block-Gauss-Seidel method or the preconditioned GMRES method.To validate the high-order numerical methods developed in this paper,simulations of 2-D rotating cylinder,2-D transonic airfoil oscillation,3-D hovering rotors,and 3-D rotating sphere flow-fields are carried out and presented at last.The numerical results are carefully compared and analyzed,proving the correctness,effectiveness,and high accuracy of the methods.The results also manage to demonstrate high-order methods' advantages when simulating complicated flowfields.Moreover,investigations on different outer boundary conditions for hovering rotor simulations are presented as well.A simple smooth procedure for the outlet speed is proposed in this thesis,which can effectively eliminate the discontinuity of the outlet speed and serve as a tool to adjust the radius of the outlet at the meantime.Through this smooth procedure,the solution near the outlet and the global convergence are effectively improved.