Variational Multiscale Methods for incompressible flows

Gravemeier, V.; Lenz, Stefan; Wall, Wolfgang A.

doi:10.1504/ijcsm.2007.016545

Cited by 16 publications

(8 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Calo has also shown an implementation of RB-VMS on a second-order finite volume code and described how to derive a weak formulation that yields an equivalent discrete equation system. Gravemeier et al [41] studied turbulent flows in a channel at Re = 180 with a RB-VMS finite element method showing the importance of higher-order polynomial approximations. Bazilevs et al [40] presented a LES-type VMS theory of turbulence and tested it on forced homogeneous turbulence, isotropic turbulence and turbulent homogeneous channel flows, stressing the superior quality of NURBS elements with respect to classical finite elements.…”

Section: Introductionmentioning

confidence: 99%

Residual-based variational multiscale simulation of free surface flows

et al. 2010

View full text Add to dashboard Cite

In this work we apply the residual-based variational multiscale method (RB-VMS) to the volume-of-fluid (VOF) formulation of free-surface flows. Using this technique we are able to solve such problems in a Large Eddy Simulation framework. This is a natural extension of our Navier-Stokes solver, which uses the RB-VMS finite element formulation, edge-based data structures, adaptive time step control, inexact Newton solvers and supports several parallel programming paradigms. The VOF interface capturing variable is advected using the computed coarse and fine scales velocity field. Thus, the RB-VMS technique can be readily applied to the free-surface solver with minor modifications on the implementation. We apply this technique to the solution of two problems where available data indicate complex free-surface behavior. Results are compared with numerical and experimental data and show that the present formulation can achieve good accuracy with minor impacts on computational efficiency.Keywords Variational multiscale method · Edge-based computations · Volume of fluid · Free surface flows

show abstract

Section: Introductionmentioning

confidence: 99%

Residual-based variational multiscale simulation of free surface flows

et al. 2010

View full text Add to dashboard Cite

show abstract

“…Calo has also shown an implementation of RB-VMS on a second-order finite volume code and described how to derive a weak formulation that yields an equivalent discrete equation system. Gravemeier et al [16] studied turbulent flows in a channel at Re = 180 with an RB-VMS finite element method showing the importance of higher-order polynomial approximations. Bazilevs et al [15] presented an LES-type VMS theory of turbulence and tested it on forced homogeneous turbulence, isotropic turbulence and turbulent homogeneous channel flows, stressing the superior quality of NURBS elements with respect to classical finite elements.…”

mentioning

confidence: 99%

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

Lins

Elias

Guerra

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

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.

show abstract

“…The VMS approach constitutes a framework for the development of comprehensive and robust formulations for the solution of multiphysics and multiscale transport problems. VMS methods have proven robust and efficient strategies for the modeling and simulation of diverse types of flow problems, as evidenced by the works reported in [15,[17][18][19] on incompressible flows, [20][21][22] on compressible flows, [23][24][25][26] on transitional and turbulent flows, [27] on reactive flows, [28] on radiative transport problems, and [29][30][31] on plasma flows. The VMS framework is ideally suited for the development of coarse-grained models, particularly as those required for the simulation of fluid flow turbulence.…”

Section: Variational Multiscale Finite Element Methodsmentioning

confidence: 99%

Algebraic approximation of sub-grid scales for the variational multiscale modeling of transport problems

Modirkhazeni

Trelles

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Variational Multiscale (VMS) Finite Element Methods (FEMs) are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems. To obtain a tractable and computationally efficient model, VMS methods often rely on a residual-based algebraic approximation of the sub-grid scales (small or unresolved features of the solution field not captured by the discretization) using a so-called intrinsic time scale matrix, which depends on the problem's overall differential operator and represents the main model parameter. A novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner (e.g., does not rely on eigenvalue computations) is presented. The method is denoted Transport-Equivalent Scaling (TES) and is based on the monolithic casting of the transport problem as a system of transient-advective-diffusive-reactive (TADR) equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux. An algebraic VMS formulation incorporating the TES method is complemented with a discontinuity-capturing (DC) approach and implemented within a FEM solver for the solution of TADR problems. The solution of the global discrete system is accomplished using a generalized-alpha time-stepper together with a globalized inexact Newton-Krylov nonlinear solver. The effectiveness of the TES formulation is verified with the simulation of benchmark incompressible, compressible, and magnetohydrodynamic flow problems. The results demonstrate that the TES method seamlessly handles incompressiblecompressible flows in a unified manner (e.g., without assessing the compressibility of the flow). The convergence process using the TES approach and a more standard approximation for the intrinsic time scales, as well as the effect of the DC approach, are also investigated. Analysis of the intrinsic time scales for a one-dimensional incompressible flow model reveals the similitudes and differences between the TES formulation and other conventional methods.

show abstract

Variational Multiscale Methods for incompressible flows

Cited by 16 publications

References 23 publications

Residual-based variational multiscale simulation of free surface flows

Residual-based variational multiscale simulation of free surface flows

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

Algebraic approximation of sub-grid scales for the variational multiscale modeling of transport problems

Contact Info

Product

Resources

About