An incompressible 3D NavierStokes method with adaptive hybrid grids
Abstract
A numerical method has been developed for the unsteady NavierStokes equations of incompressible flow in three dimensions. The momentum equations, combined with a pressure correction equation, are solved employing a nonstaggered grid which results in a simpler formulation compared to the classical approach of using staggered meshes. The momentum equations are solved explicitly using a finite volume algorithm, while the pressure Poisson equation is discretized using the Galerkin finite element method and implicitly solved. The grid is formed with hybrid (prismatic/tetrahedral) elements. Equation adaptation is utilized, the NavierStokes equations are solved in the prismatic region, which includes the viscous region, and the Euler equations are solved in the tetrahedral region, which is inviscid. Adaptive local grid refinement of the prism and tetrahedral cells is employed in order to optimize the mesh to the flow solution. Validation of the algorithm is performed using experimental and other numerical data, and demonstrate the accuracy and robustness of the unsteady threedimensional method. An additional study is conducted using an existing twodimensional incompressible NavierStokes solver. The twodimensional solver is applied to predict the hydrodynamic forces on a circular cylinder due to reversing flows.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 1995
 Bibcode:
 1995PhDT.........3C
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 Computerized Simulation;
 Incompressible Flow;
 NavierStokes Equation;
 Three Dimensional Flow;
 Finite Element Method;
 Flow Equations;
 Galerkin Method;
 Inviscid Flow;
 Momentum Theory;
 Poisson Equation;
 Unsteady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer