A tensor artificial viscosity using a finite element approach

Kolev, Tzanio V.; Rieben, Robert N.

doi:10.1016/j.jcp.2009.08.010

Cited by 74 publications

(61 citation statements)

References 20 publications

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“…Velocities are defined at mesh nodes and density and internal energy are defined at the zone centers using a piecewise constant profile. Artificial viscosity is used to suppress spurious oscillations [11] following the remap phase of the calculation, where the Lagrangian solution is remapped back to a non-Lagrangian mesh, and is fully second order. The original method is given in by Sharp and Baron [12].…”

Section: Computational Setupmentioning

confidence: 99%

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Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface

2011

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A computational study of the Richtmyer-Meshkov instability for an inclined interface is presented. The study covers experiments to be performed in the Texas A&M inclined shock tube facility. Incident Mach numbers from 1.2 to 2.5, inclination angles from 30 to 60 degrees, and gas pair Atwood numbers of ~0.67 and ~0.95 are used in this parametric study containing 15 unique combinations of these parameters. Qualitative results are examined through a time series of density plots for multiple combinations of the parameters listed above, and qualitative effects of each of the parameters is discussed. The interface mixing width growth rate is determined for various combinations of the above parameters. A new model for the mixing width growth rate is proposed using the interface geometry and wave velocities calculated using 1D gas dynamic equations. This model uses the transmitted wave velocity for the characteristic velocity and an initial offset time based on the travel time of strong reflected waves. The new model is compared to the Richtmyer Impulsive model and shown to better predict the initial linear mixing width growth rate.2

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Section: Computational Setupmentioning

confidence: 99%

“…Since the impulsive model matched different Atwood number cases well the gas pair ratio parameter, Atwood number, was not changed. (11) : ;…”

Section: Inclined Interface Impulsive Modelmentioning

confidence: 99%

Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface

2011

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“…Artificial viscosity smooths a shock over several zones, where physically the shock would have behaved as a discontinuity. Traditionally, this has been a scalar quantity that activates in regions with high gradients [38], but this method has not performed well in general cases where the shock wave is not aligned with the mesh [24].…”

Section: Tensor Artificial Viscositymentioning

confidence: 99%

“…Specifically we implemented the general finite element based tensor artificial viscosity formulation of Kolev and Rieben [24]. This formulation is general enough to easily allow for high order velocity field representations.…”

Section: Tensor Artificial Viscositymentioning

confidence: 99%

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High Order Finite Elements for Lagrangian Computational Fluid Dynamics

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Curvilinear finite elements for Lagrangian hydrodynamics

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Ellis

Kolev

et al. 2011

Numerical Methods in Fluids

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SUMMARYWe have developed a novel high-order, energy conserving approach for solving the Euler equations in a moving Lagrangian frame, which is derived from a general finite element framework. Traditionally, such equations have been solved by using continuous linear representations for kinematic variables and discontinuous constant fields for thermodynamic variables; this is the so-called staggered grid hydro (SGH) method. From our general finite element framework, we can derive several specific high-order discretization methods and in this paper we introduce a curvilinear finite element method which uses continuous bi-quadratic polynomial bases (the Q 2 isoparametric elements) to represent the kinematic variables combined with discontinuous (mapped) bi-linear bases to represent the thermodynamic variables. We consider this a natural generalization of the SGH approach and show that under simplifying low-order assumptions, we exactly recover the classical SGH method. We review the key parts of the discretization framework and demonstrate several practical advantages to using curvilinear finite elements for Lagrangian shock hydrodynamics, including: the ability to more accurately capture geometrical features of a flow region, significant improvements in symmetry preservation for radial flows, sharper resolution of a shock front for a given mesh resolution including the ability to represent a shock within a single zone and a substantial reduction in mesh imprinting for shock waves that are not aligned with the computational mesh.

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A tensor artificial viscosity using a finite element approach

Cited by 74 publications

References 20 publications

Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface

Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface

High Order Finite Elements for Lagrangian Computational Fluid Dynamics

Curvilinear finite elements for Lagrangian hydrodynamics

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