A theoretical framework for discontinuity capturing: joining variational multiscale analysis and variation entropy theory
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Publication:2175083
DOI10.1016/j.cma.2019.112664zbMath1441.49016OpenAlexW2979496835WikidataQ127099774 ScholiaQ127099774MaRDI QIDQ2175083
M. F. P. ten Eikelder, Yuri Bazilevs, Ido Akkerman
Publication date: 28 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2019.112664
variational multiscale methodisogeometric analysisdiscontinuity capturing operatorsTVD propertyvariation entropyvariation entropy residual-based
Variational inequalities (49J40) Hyperbolic conservation laws (35L65) Applications to the sciences (65Z05)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- A maximum-principle preserving \(C^0\) finite element method for scalar conservation equations
- Implementation of the entropy viscosity method with the discontinuous Galerkin method
- Isogeometric analysis of free-surface flow
- Entropy viscosity method for nonlinear conservation laws
- A consistent approximate upwind Petrov-Galerkin method for convection- dominated problems
- Stabilized methods for compressible flows
- Enforcement of constraints and maximum principles in the variational multiscale method
- An acoustic-convective splitting-based approach for the Kapila two-phase flow model
- A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes --application to vortex shedding
- Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations
- Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
- SUPG finite element computation of inviscid supersonic flows with \(YZ \beta\) shock-capturing
- New non-oscillatory central schemes on unstructured triangulations for hyperbolic systems of conservation laws
- Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method
- Residual-based variational multiscale simulation of free surface flows
- On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. II: Analysis for \(P_{1}\) and \(Q_{1}\) finite elements
- Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and \(YZ\beta\) shock-capturing
- The role of continuity in residual-based variational multiscale modeling of turbulence
- On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I: A review
- Time dependent subscales in the stabilized finite element approximation of incompressible flow problems
- High resolution schemes for hyperbolic conservation laws
- A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
- A new finite element formulation for computational fluid dynamics. IV: A discontinuity-capturing operator for multidimensional advective-diffusive systems
- A new finite element formulation for computational fluid dynamics. II. Beyond SUPG
- Entropy functions for symmetric systems of conservation laws
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
- What are \(C\) and \(h\)?: Inequalities for the analysis and design of finite element methods
- The variational multiscale method -- a paradigm for computational mechanics
- Towards the ultimative conservative difference scheme. V: A second-order sequel to Godunov's method
- A well-balanced positivity preserving ``second-order scheme for shallow water flows on unstructured meshes
- Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows
- The corrected operator splitting approach applied to a nonlinear advection-diffusion problem
- A comparative study of different sets of variables for solving compressible and incompressible flows
- Variationally derived discontinuity capturing methods: fine scale models with embedded weak and strong discontinuities
- Correct energy evolution of stabilized formulations: the relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier-Stokes equations
- \textsc{tIGAr}: automating isogeometric analysis with \textsc{FEniCS}
- Variation entropy: a continuous local generalization of the TVD property using entropy principles
- Correct energy evolution of stabilized formulations: the relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective-diffusive context
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- SUPG finite element computation of compressible flows with the entropy and conservation variables formulations
- On the computation of the Baer-Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid-structure interactions
- Improving stability of stabilized and multiscale formulations in flow simulations at small time steps
- A space-time formulation for multiscale phenomena
- Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
- Algebraic Mesh Quality Metrics
- Recent Advances in Fluid–Structure Interaction Simulations of Wind Turbines
- A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws
- First order quasilinear equations with boundary conditions
- On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes
- Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
- Sensitivity of the scale partition for variational multiscale large-eddy simulation of channel flow
- High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
- Total-Variation-Diminishing Time Discretizations
- Centred TVD schemes for hyperbolic conservation laws
- YZβ discontinuity capturing for advection‐dominated processes with application to arterial drug delivery
- Variational Multiscale Analysis: the Fine‐scale Green’s Function, Projection, Optimization, Localization, and Stabilized Methods
- Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations
- FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
- A natural derivation of discontinuity capturing operator for convection-diffusion problems
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