Computation of the Three-Dimensional Nonlinear Flow Around a Body in or Near the Free Surface

2008 ◽  
Author(s):  
Chi Yang ◽  
Haidong Lu ◽  
Rainald Lo¨hner ◽  
William C. Sandberg
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Nonlinear Flow ◽  
Advection Equation ◽  
Flow Solver ◽  
Surface Equation ◽  
Flow Around A Body

An unstructured grid-based, parallel incompressible flow solver has been developed for solving the three-dimensional non-linear flow around a body in or near the free surface. The incompressible Euler/Navier-Stokes equations are solved together with or without the free surface equation. The overall scheme combines a finite-element, equal-order, projection-type three-dimensional incompressible flow solver with a finite element, two-dimensional advection equation solver for the free surface equation. The solution is marched in time until a steady state is reached. The computer code developed based on the method described above has been applied to the simulation study of the three-dimensional nonlinear flow around a flying fish when it swims underwater, taxis on the free surface, and glides above water.

Numerical Simulation of Transient Free Surface Flows Using a Moving Mesh Technique

2006 ◽  
Vol 73 (6) ◽  
pp. 1017-1025 ◽  
Author(s):  
Laura Battaglia ◽  
Jorge D’Elía ◽  
Mario Storti ◽  
Norberto Nigro
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Surface Flows ◽  
Flow Domain ◽  
Convection Dominated

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, “A Multidimensional Upwind Scheme With no Crosswind Diffusion,” in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19–35, and Brooks, A. N., and Hughes, T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, “Stablized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, “Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,” Comput. Methods Appl. Mech. Eng., 95, pp. 221–242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

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