Parallel Edge-Based Inexact Newton Solution of Steady Incompressible 3D Navier-Stokes Equations

Coutinho

2007

Self Cite

100

SUMMARYFree-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbours and coastal areas. The computation of such highly nonlinear flows is challenging since free-surfaces commonly present merging, fragmentation and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function which is transported in a flow field. In this work we present a three-dimensional parallel edge-based incompressible SUPG/PSPG finite element method to cope with free-surface problems with volume-of-fluid (VOF) extensions to track the evolving free surface. The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. We studied variants of this formulation, considering the effects of discontinuity capturing and a particular tangent transformation designed to increase interface sharpness. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method were tested with several validation problems.

Section: Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stabilized edge‐based finite element simulation of free‐surface flows

Coutinho

2007

Self Cite

100

“…The computational domain follows the dimensions described in [32] and the mesh is formed by 446 662 linear tetrahedra, 1 010 367 edges and 81 991 nodes. The Reynolds number is based on the diameter of the cylinder, free-stream velocity and viscosity of the fluid.…”

Section: Vortex Shedding Around a Circular Cylinder At Re = 100mentioning

confidence: 99%

Edge‐based finite element implementation of the residual‐based variational multiscale method

Lins

Guerra

et al. 2008

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SUMMARYIn this work we extend our edge-based stabilized finite element incompressible flow solver to turbulence modeling with the residual-based variational multiscale (RB-VMS) method. Using the advective-form of the convection term of the Navier-Stokes equations, RB-VMS is implemented as a straightforward extension of standard stabilized methods with a modified advective velocity. This requires minimum modification of the existing highly optimized code. Two test cases were solved to assess accuracy and performance of the present implementation. First, the laminar incompressible flow past a circular cylinder at Re = 100 and second, the fully turbulent incompressible flow in a lid-driven cubic cavity at Re=12 000. Comparisons were made with standard stabilized finite element formulations, highly resolved numerical simulations and experimental data. Results have shown that the present implementation is able to achieve reasonable accuracy without performance degradation in different flow regimes.

“…Most of the computational effort spent in the solution phase is devoted to matrix-vector products. In order to compute such operations more efficiently, we have used an edge-based data structure as detailed in [43]. According to Ribeiro and Coutinho [36], this data structure, when applied to problems as those described in this work, is able to reduce indirect memory access, memory requirements to hold the coefficients of the stiffness matrices and the number of floating point operations when compared with other traditional data structures such as element by element or compressed sparse row.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…Time integration is a predictor-multicorrector algorithm with adaptive timestepping by a proportional-integral-Derivative (PID) controller (further details available in [42]). Within the flow solution loop, the multi-correction steps correspond to the inexact-Newton method as described in [43]. In this method, the tolerance of the linear solver is adapted according to the history of the solution residua.…”

Section: Solution Proceduresmentioning

confidence: 99%

Stabilized edge‐based finite element computation of gravity currents in lock‐exchange configurations

Paraizo

Coutinho

2008

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SUMMARYModeling of gravity current flows is important in many problems of science and engineering. Gravity currents are primarily horizontal flows driven by a density difference of few per cents. This phenomenon occurs in many scales in nature, such as ocean and marine flows, sea breeze formation, avalanches, turbidite flows, etc. Most of the gravity current simulations employ structured grid or spectral methods. In this work, we simulate gravity-driven flows by a parallel stabilized edge-based finite element code with particular emphasis on the simulation of the lock-exchange problem for planar and cylindrical configurations. Our results are validated against other highly resolved numerical simulations and experiments.