6 research outputs found
Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media
In this paper, we study the unconditional convergence and error estimates of
a Galerkin-mixed FEM with the linearized semi-implicit Euler time-discrete
scheme for the equations of incompressible miscible flow in porous media. We
prove that the optimal error estimates hold without any time-step
(convergence) condition, while all previous works require certain time-step
condition. Our theoretical results provide a new understanding on commonly-used
linearized schemes for nonlinear parabolic equations. The proof is based on a
splitting of the error function into two parts: the error from the time
discretization of the PDEs and the error from the finite element discretization
of corresponding time-discrete PDEs. The approach used in this paper is
applicable for more general nonlinear parabolic systems and many other
linearized (semi)-implicit time discretizations
Finite element model for three-dimensional compressible turbulent flows
Due to the complexity of the Navier-Stokes equations, numerical methods are widely used to analyze the flows. In this thesis, we establish a finite element model for three-dimensional compressible turbulent flows. We modified an in-house code in order to use several types of elements in a computational domain. We used four types of elements in our mesh: the 8-node hexahedron, the 4-node tetra, the 6-node prism, and the 5-node pyramid. The original code used only the 4-node tetra elements. We used the Streamline Upwind/Petrov-Galerkin stabilization technique with a shock capturing operator.
We validated the code with benchmark tests using the 3D Naca0012 model and the DLR F11 model. We used different sets of Reynolds numbers, Mach numbers, and angles of attack to test the code and compare our results with other numerical and experimental results. Because of the strong nonlinearities with the increase of the angle of attack, we need to set up a solution strategy to avoid divergence of the solution. The tests of verification and validation show that the results we obtained are comparable to those of the references