A palette of fine-scale eddy viscosity and residual-based models for variational multiscale formulations of turbulence

Oberai, Assad A.; Hughes, Thomas J.R.

doi:10.1007/s00466-015-1242-2

Cited by 3 publications

(1 citation statement)

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“…Interested readers are referred to [1, 20, 59] for comprehensive reviews. In this section, we invoke the residual-based VMS method [5, 95] to construct a formulation for the continuum problem derived in Section 2. Here, and in what follows, we restrict our discussion to the isothermal condition 1 .…”

Section: Variational Multiscale Analysismentioning

confidence: 99%

A unified continuum and variational multiscale formulation for fluids, solids, and fluid–structure interaction

Marsden

2018

Computer Methods in Applied Mechanics and Engineering

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We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-α method is applied for temporal discretization. A segregated algorithm for the nonlinear solver, based on the original idea introduced in [107], is carefully analyzed. Second, we apply the new formulation to construct a novel unified formulation for fluid-solid coupled problems. The variational multiscale formulation is utilized for spatial discretization in both fluid and solid subdomains. The generalized-α method is applied for the whole continuum body, and optimal high-frequency dissipation is achieved in both fluid and solid subproblems. A new predictor multi-corrector algorithm is developed based on the segregated algorithm. The efficacy of the new formulations is examined in several benchmark problems. The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models.

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