This paper extends earlier research in numerical analysis and computational fluid dynamics (CFD) to obtain a novel finite element method for transient 3-D incompressible Navier-Stokes equations, along with efficient, parallelizable algorithms to cary out an implementation of the method in such a fashion as to be useful in mainstream industrial settings. The approach is based on a flexible operator-splitting technique due to one of the authors that allows the introduction of increasingly complex physics one step at a time. The approach should also allow treating potential flow, Euler flow, and Navier-Stokes flow simultaneously in different parts of the flow region. Parallelization is achieved through domain decomposition techniques. A new type of Eulerian time discretization is employed to increase accuracy and maintain computational efficiency.This new finite element procedure employs alternating-direction operator splittings in conjuction with Strang-type splittings to model problems of increasing complexity in a step-by-step and natural manner. Later, it can be extended to include additional operators e.g. for turbulence modeling, chemical reactions, etc. In addition to being practical from the standpoint of software design and of engineering analysis, its development and implementation allows the use of specialized numerical methods for the solution of each phys-*Ph.D student, IN 47907; Associate Fellow AIAA.ical phenomenon modeled. The scheme employs a characteristic-Galerkin method for the numerical treatment of the nonlinear advection operator. Non-overlapping domain decomposition schemes are employed for the solution of linear Stokes-type subproblems and for the matching of the inviscid and viscous solutions in different subdomains. These problems are solved by Bramble-Pasciakt Schatz wirebasket domain decomposition methods in a stabilized mixed finite element method* formulation. The scheme is coupled to an exf isting grid generator code that provides globally unstructured, but locally structured grids, within each subdomain.
Preliminaries
MotivationThis paper concerns extension of earlier research done in applied mathematics, numerical analysis, and computational fluid dynamics (CFD) to produce a novel application of the finite element method to the unsteady 3-D incompressible Navier-Stokes (NS) equations of fluid dynamics. The long-term goal of this project is to render CFD simulations feasible in a mainstream industrial setting, where there is a need for software to handle arbitrarily-complex shapes -other than airfoils and wings.The finite element method has been established as the method of choice in industrial structural mechanics applications. No other numerical method possesses the versatility for handling complicated geometrical shapes and associated boundary conditions. The method handles unstructured grids in a natural manner.Aside from geometric considerations, other important areas of concern are the cost and the feasibility of the computations. As a practical matter, 1 Downloaded by Stanford...
