Weak imposition of Dirichlet boundary conditions in fluid mechanics

By Yuri Bazilevs, Thomas J. R. Hughes. 2007

513 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1ed1ca3a603bc62aac06570477b3204bdbe605b5

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In Computational Mechanics

Citations in the corpus

Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow (2006, background): “The class of residual-based multiscale methods may be thought of as stabilized methods, such as SUPG (see Brooks and Hughes [4]), extended to the nonlinear realm.”
Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics (2012, background): “[22,23,29] for the derivation and discussion of weak boundary conditions for the equations of fluid mechanics.”
Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method (2010, methodology): “Weak boundary conditions, which are based on Nitsche’s approach [41] and concepts from Discontinuous Galerkin methods, were proposed in [6] for the advection diffusion and incompressible Navier–Stokes equations, and further enhanced in [8,9].”
ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS (2013, methodology): “Utilzing Nitsche’s method allows us to account for these layers in a stable and consistent manner without having to directly resolve them [2, 3, 4].”
Discretizations in isogeometric analysis of Navier-Stokes flow (2011, unknown): “Boundary Conditions For simplicity we impose the Dirichlet boundary conditions in (1c) strongly as opposed to the weak enforcement suggested in [14, 15].”
Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows (2007, methodology): “Alternatively, one may enforce the no-slip conditions weakly by augmenting the discrete formulation with terms that enforce Dirichlet conditions as Euler–Lagrange conditions (see [6,7]).”
Isogeometric fluid-structure interaction: theory, algorithms, and computations (2008, background): “For example, condition (110) may be imposed weakly (see, e.g., [ 6 ,7]) by constructing additional terms on the fluid-solid interface using ideas emanating from discontinuous Galerkin methods.”
A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes (2012, unknown): “This definition of the weighting term a is very similar to the one used in the weak imposition of boundary conditions in [34], the main difference being that in our case is accompanied with a 1 2 factor.”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, background): “A typical benchmark test [130,131] for adaptive refinement is sketched in Fig.”
Locally conservative, stabilized finite element methods for variably saturated flow (2008, background): “Another approach is to enforce Dirichlet boundary conditions weakly in the original finite element solution as in [25, 63].”
On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review (2007, background): “Burman [10] and Hughes and Bazilevs [5] demonstrated numerically that using weakly imposed Dirichlet boundary conditions reduces spurious oscillations at outflow boundaries considerably.”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, unknown): “For optimal convergence, the size of the stabilization parameters τS and τN is proportional to the material properties, here the Lamé constants λ and ν, inversely proportional to the characteristic element width h, and dependent on constants CS and CN , influenced by the polynomial degree p [78,79]:”
An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves (2014, methodology): “Keywords Fluid–structure interaction, Bioprosthetic heart valve, Immersogeometric analysis, Isogeometric analysis, Nitsche’s method, Weakly enforced boundary conditions Disciplines Biomedical Devices and Instrumentation | Biomedical Engineering and Bioengineering | Computer-Aided Engineering and Des”