Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier–Stokes simulations

Cousins, Benjamin; Rebholz, Leo G.; Wilson, Nicholas E.

doi:10.1016/j.amc.2011.05.111

Cited by 7 publications

(10 citation statements)

References 16 publications

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“…We compute with ..P 3 / 3 , P d isc 2 / Scott Vogelius (SV) elements on a barycenter refined tetrahedralization of the domain, via the method of [30], and a uniform time step of D 0.025 is used to compute the solutions up to end-time T D 10. Of the three, the VQ-based filter appears to resolve it best; a zoomed in look at the streamribbons near the step in Figure 11 shows a more refined picture of its eddy separation and matches the solution of [31] qualitatively well. For the direct numerical simulation of this problem that was performed in [31], the total spatial DOFs needed to resolve this flow was 1,282,920.…”

Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 80%

“…This problem is a 3D analog of the 2D step problem presented previously, and a diagram of the flow domain is given in Figure 9; the channel is 10 40 10 with a 10 1 1 block on the bottom of the channel, five units in from the inlet. This flow was studied in [31], and the correct behavior at T D 10 is for an eddy to have detached from behind the step and moved down the channel and a new eddy to form. An inflow=outflow condition is enforced, and the initial condition is the solution of the Re D 50 steady flow.…”

Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 99%

“…No-slip boundary conditions are enforced on the channel walls and on the step. For the direct numerical simulation of this problem that was performed in [31], the total spatial DOFs needed to resolve this flow was 1,282,920. We compute with ..P 3 / 3 , P d isc 2 / Scott Vogelius (SV) elements on a barycenter refined tetrahedralization of the domain, via the method of [30], and a uniform time step of D 0.025 is used to compute the solutions up to end-time T D 10.…”

Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 99%

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Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering

Bowers

Rebholz

Takhirov

et al. 2012

Numerical Methods in Fluids

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SUMMARY We study the adaptive nonlinear filtering in the Leray regularization model for incompressible, viscous Newtonian flow. The filtering radius is locally adjusted so that resolved flow regions and coherent flow structures are not ‘filtered out’, which is a common problem with these types of models. A numerical method is proposed that is unconditionally stable with respect to time step and decouples the problem so that the filtering becomes linear at each time step and is decoupled from the system. Several numerical examples are given that demonstrate the effectiveness of the method. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 80%

Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 99%

Section: D Channel Flow Over a Forward-backward Stepmentioning

confidence: 99%

See 1 more Smart Citation

Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering

Bowers

Rebholz

Takhirov

et al. 2012

Numerical Methods in Fluids

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“…We use instead a quartic inflow profile, given below by (3.13), and for simplicity also enforce this condition at the outlet. The correct physical behavior for this flow problem, which was resolved by Cousins et al [7], is that by T ¼ 10, an eddy forms behind the step, detaches and moves into the flow, and another eddy forms.…”

Section: Methodsmentioning

confidence: 99%

Assessment of a vorticity based solver for the Navier–Stokes equations

Benzi

Olshanskii

Rebholz

et al. 2012

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tWe investigate numerically a recently proposed vorticity based formulation of the incompressible Navier-Stokes equations. The formulation couples a velocity-pressure system with a vorticity-helicity system, and is intended to provide a numerical scheme with enhanced accuracy and superior conservation properties. For a few benchmark problems, we study the performance of a finite element method for this formulation and compare it with the commonly used velocity-pressure based finite element method. It is shown that both steady and unsteady discrete problems in the new formulation admit simple decoupling strategies followed by the application of iterative solves to auxiliary subproblems. Further, we compare several iterative strategies to solve the discrete problems and study the interplay between the choice of stabilization parameters in the finite element method and the efficiency of linear algebra solvers.

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“…The [2] considered two kinds of two-level stabilized finite element methods based on local Gauss integral technique for the two-dimensional stationary Navier-Stokes equations approximated by the lowest equal-order elements which do not satisfy the inf-sup condition. A finite element scheme for the 3D Navier-Stokes equations (NSE) through the use of Scott-Vogelius elements [3], enforces point wise the solenoidal constraints for velocity and vorticity. Tavelli and Dumbser proposed a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes [4].…”

Section: Introductionmentioning

confidence: 99%