On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes

Principe, Javier; Codina, Ramon

doi:10.1016/j.cma.2009.08.011

Cited by 28 publications

(21 citation statements)

References 51 publications

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“…If elements of oder p are used (p is not the pressure, here), c 1 must be replaced by c 1 p 4 and c 2 by c 2 p. For anisotropic elements, the definition of h within each element is not obvious. A possibility is explained in [51].…”

Section: −1 Cmentioning

confidence: 99%

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Colomés

Badia

Codina

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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101

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In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor-Green vortex problem and the turbulent flow in a channel. We compare the results obtained using the different VMS models and against a classical LES scheme based on filtering and the Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these results, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.

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Section: −1 Cmentioning

confidence: 99%

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Colomés

Badia

Codina

et al. 2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

101

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show abstract

“…For our purpose, with Vlasov-or transport-type equations (also for the case of Euler and Navier-Stokes problems as in Johnson and Saranen (1986), it suffices to choose 5 ~ h. For Elastoplast-plasticity and some other models, arising, for example, in mechanical engineering problems, the term involving the parameter 5 will have a more involved and different form. For details about the stabilization parameter see Principe and Codina (2010) and the references therein.…”

Section: 1 S Tr E a M Lin E D Iffu Sio N Fo R M A X W E Ll E Q U Amentioning

confidence: 99%

On a Canonical Form for Maxwell Equations and Convergence of Finite Element Schemes for a Vlasov-Maxwell System

Asadzadeh

2014

Journal of Computational and Theoretical Transport

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O n a C a n o n ic a l F o rm fo r M a x w e ll E q u a tio n s a n d C o n v e r g e n c e o f Finite E le m e n t S c h e m e s fo r a V la s o v -M a x w e ll S ystem M. A sa d zad eh _____________________________________________This work is a swift introduction to the nature of governing laws involved in the Maxwell equations. We then approximate a "one and one-half' dimensional relativistic Vlasov-Maxwell (VM) system using streamline diffusion finite element method. In this geometry d'Alembert representation for the fields functions guarantees the existence of a unique solution of the Maxwell equations. The VM system is then approximated using the streamline diffusion finite element method. In this part we derive some sta bility inequalities and optimal a priori error estimates due to the maximal available regularity of the exact solution. In this article we introduce some basic properties of the equations in the Maxwell's system and point out the special roles played by the field functions.We then consider a one and one-and-half dimensional, relativistic, VlasovMaxwell (VM) system. In this geometry we derive closed form solutions for the field equations represented in d'Alembert's formulas. This is the simplest possible to derive the existence of a unique solution for the field functions in Maxwell's equation. There is no d'Alembert representation in higher dimen sions. Our main concern will be approximation of the VM system by a semiclassical finite element approach: the streamline diffusion (SD) method. Both

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“…We will however not proceed in this direction and favor an alternate approach, to which we now turn. Based upon the observation (27) for the "ideal" space V ε H , we may use the stabilization term (28) rather than (26). In contrast to (26), the quantity (28) is also well defined on V ε H,h .…”

Section: The Classical Msfem and Its Stabilized Versionmentioning

confidence: 99%

A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media

2017

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The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the simultaneous presence of both heterogeneity of scales and strong advection. Classical MsFEM methods are compared with adjusted MsFEM methods, stabilized versions of the methods, and a splitting method that treats the multiscale diffusion and the strong advection separately.

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On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes

Cited by 28 publications

References 51 publications

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

On a Canonical Form for Maxwell Equations and Convergence of Finite Element Schemes for a Vlasov-Maxwell System

A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media

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