A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces

Abstract In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.

[1]  Eugenio Oñate,et al.  A finite element formulation for incompressible flow problems using a generalized streamline operator , 1997 .

[2]  T. Tezduyar,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests , 1992 .

[3]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[4]  E. Oñate,et al.  On the pseudomaterial approach for the analysis of transient forming processes , 1995 .

[5]  J. Altenbach.  Zienkiewicz, O. C., The Finite Element Method. 3. Edition. London. McGraw‐Hill Book Company (UK) Limited. 1977. XV, 787 S. , 1980 .

[6]  Guillermo Hauke,et al.  a Unified Approach to Compressible and Incompressible Flows and a New Entropy-Consistent Formulation of the K - Model. , 1994 .

[7]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[8]  Antonio Huerta,et al.  Viscous flow with large free surface motion , 1988 .

[9]  F. Stella,et al.  A vorticity-velocity method for the numerical solution of 3D incompressible flows , 1993 .

[10]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[11]  O. Pironneau,et al.  Navier-Stokes equations with imposed pressure and velocity fluxes , 1995 .

[12]  T. Hughes,et al.  Convergence analyses of Galerkin least-squares methods for symmetric advective-diffusive forms of the Stokes and incompressible Navier-Stokes equations , 1993 .

[13]  De Sampaio,et al.  A Petrov–Galerkin formulation for the incompressible Navier–Stokes equations using equal order interpolation for velocity and pressure , 1991 .

[14]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems , 1986 .

[15]  Thomas J. R. Hughes,et al.  The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces , 1987 .

[16]  Finite element solution of the incompressible Navier-Stokes equations by a Helmholtz velocity decomposition , 1991 .

[17]  O. C. Zienkiewicz,et al.  Incompressibility without tears—HOW to avoid restrictions of mixed formulation , 1991 .

[18]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .