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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

Le schema est base sur la resolution des equations d'ecoulement potentiel pour des blocs individuels representant des sous-volumes du champ d'ecoulement

A block-structured solution scheme is developed for the solution of Euler equations for steady three-dimensional transonic flows*. The Euler equations are expressed in terms of Clebsch variables w = v + Svn. The resulting set of equations for conservation of mass, entropy (5) and the Clebsch variable j\ are solved using a block-based relaxation scheme. The flowfield is divided into a series of individual blocks representing local regions of the flowfield. The employed grid generation scheme provides local refinement of each block yet ensures one-to-one matching of grid points on the surfaces of adjoining blocks. For each of the blocks, either potential or Euler equations can be solved. For every block, the conservation of mass equation is solved to determine . For blocks with rotationality, two additional equations for determining S and T\ are solved. In this paper, the basic steps of the developed solution scheme are presented. The computational considerations involved in utilizing the present scheme are demonstrated for several two-dimensional sample problems.