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Hyea-Hyun Kim, Eric Chung, C. Lee (2013)
A Staggered Discontinuous Galerkin Method for the Stokes SystemSIAM J. Numer. Anal., 51
P. Causin, Jean-Frédéric Gerbeau, F. Nobile (2005)
Added-mass effect in the design of partitioned algorithms for fluid-structure problemsComputer Methods in Applied Mechanics and Engineering, 194
Eric Chung, C. Lee (2012)
A staggered discontinuous Galerkin method for the curl–curl operatorIma Journal of Numerical Analysis, 32
Eric Chung, Q. Du, J. Zou (2003)
Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous MediaSIAM J. Numer. Anal., 41
P Blanc, R Eymard, R Herbin (2005)
A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensionsInt. J. Finite Vol., 2
C. Peskin, B. Printz (1993)
Improved Volume Conservation in the Computation of Flows with Immersed Elastic BoundariesJournal of Computational Physics, 105
Eric Chung, P. Ciarlet, T. Yu (2013)
Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian gridsJ. Comput. Phys., 235
C. Peskin (2002)
The immersed boundary methodActa Numerica, 11
Eric Chung, Bernardo Cockburn, G. Fu (2014)
The Staggered DG Method is the Limit of a Hybridizable DG MethodSIAM J. Numer. Anal., 52
Eric Chung, P. Ciarlet (2013)
A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materialsJ. Comput. Appl. Math., 239
J. Carrero, Bernardo Cockburn, D. Schötzau (2005)
Hybridized globally divergence-free LDG methods. Part I: The Stokes problemMath. Comput., 75
P. Blanc, R. Eymard, R. Herbin (2005)
A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations, 2
Bernardo Cockburn, Chi-Wang Shu (1998)
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion SystemsSIAM Journal on Numerical Analysis, 35
Eric Chung, C. Lam, J. Qian (2015)
A staggered discontinuous Galerkin method for the simulation of seismic waves with surface topographyGeophysics, 80
B Cockburn, J Gopalakrishnan, NC Nguyen, J Peraire, F-J Sayas (2011)
Analysis of an HDG method for Stokes flowMath. Comput., 80
F. Harlow, J. Welch (1965)
Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free SurfacePhysics of Fluids, 8
Hyea-Hyun Kim, Eric Chung, C. Lee (2014)
FETI-DP preconditioners for a staggered discontinuous Galerkin formulation of the two-dimensional Stokes problemComput. Math. Appl., 68
(1989)
A three - dimensional computational method for blood flow in the heart . I . Immersed elastic fibers in a viscous incompressible fluid
M. Tavelli, M. Dumbser (2016)
A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshesJ. Comput. Phys., 319
D. Boffi, L. Gastaldi, L. Heltai (2007)
NUMERICAL STABILITY OF THE FINITE ELEMENT IMMERSED BOUNDARY METHODMathematical Models and Methods in Applied Sciences, 17
M. Tavelli, M. Dumbser (2014)
A staggered semi-implicit discontinuous Galerkin method for the two dimensional incompressible Navier-Stokes equationsAppl. Math. Comput., 248
Bernardo Cockburn, G. Kanschat, D. Schötzau (2004)
A locally conservative LDG method for the incompressible Navier-Stokes equationsMath. Comput., 74
Eric Chung, B. Engquist (2005)
Convergence Analysis of Fully Discrete Finite Volume Methods for Maxwell's Equations in Nonhomogeneous MediaSIAM J. Numer. Anal., 43
B. Boersma (2005)
A staggered compact finite difference formulation for the compressible Navier-Stokes equationsJournal of Computational Physics, 208
Eric Chung, Bernardo Cockburn, G. Fu (2015)
The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes FlowJournal of Scientific Computing, 66
Zhilin Li, L. Xiao, Qin Cai, Hongkai Zhao, R. Luo (2015)
A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditionsJournal of computational physics, 297
C. Peskin (1972)
Flow patterns around heart valves: A numerical methodJournal of Computational Physics, 10
C. Peskin (1977)
Numerical analysis of blood flow in the heartJournal of Computational Physics, 25
D. Boffi, L. Gastaldi (2014)
Discrete models for fluid-structure interactions: the Finite Element Immersed Boundary MethodarXiv: Numerical Analysis
N. Nguyen, J. Peraire, Bernardo Cockburn (2011)
An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equationsJ. Comput. Phys., 230
Ronald Fedkiw (2007)
The immersed interface method. Numerical solutions of PDEs involving interfaces and irregular domainsMath. Comput., 76
ET Chung, CS Lee (2012)
A staggered discontinuous Galerkin method for the convection–diffusion eqnarrayJ. Numer. Math., 20
P. Houston, D. Schötzau, Xiaoxi Wei (2009)
A Mixed DG Method for Linearized Incompressible MagnetohydrodynamicsJournal of Scientific Computing, 40
J. Stockie, B. Wetton (1999)
Analysis of Stiffness in the Immersed Boundary Method and Implications for Time-Stepping SchemesJournal of Computational Physics, 154
M. Tavelli, M. Dumbser (2014)
A staggered space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations on two-dimensional triangular meshesarXiv: Numerical Analysis
Siu Cheung, Eric Chung, Hyea-Hyun Kim, Y. Qian (2015)
Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equationsJ. Comput. Phys., 302
Eric Chung, B. Engquist (2009)
Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher DimensionsSIAM J. Numer. Anal., 47
Khosro Shahbazi, P. Fischer, C. Ethier (2007)
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equationsJ. Comput. Phys., 222
D Boffi, L Gastaldi, L Heltai (2004)
Progress in Engineering Computational Technology
Bernardo Cockburn, G. Kanschat, D. Schötzau, C. Schwab (2002)
Local Discontinuous Galerkin Methods for the Stokes SystemSIAM J. Numer. Anal., 40
Jian‐Guo Liu, Chi-Wang Shu (1999)
A High-Order Discontinuous Galerkin Method for 2D Incompressible FlowsJournal of Computational Physics, 160
D. Boffi, L. Gastaldi, L. Heltai, Stirling Publications (2003)
A finite element approach to the immersed boundary method
Eric Chung, B. Engquist (2006)
Optimal Discontinuous Galerkin Methods for Wave PropagationSIAM J. Numer. Anal., 44
D. Schötzau, C. Schwab, A. Toselli (2002)
Mixed hp-DGFEM for Incompressible FlowsSIAM J. Numer. Anal., 40
(2013)
Conditions for superconvergence of HDGmethods for Stokes flow
In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid–structure interaction problems. We will use the immersed boundary method to model the fluid–structure interaction, while the fluid flow is governed by the incompressible Navier–Stokes equations. The immersed boundary method is proven to be a successful scheme to model fluid–structure interactions. To ensure mass conservation, we will use the staggered discontinuous Galerkin method to discretize the incompressible Navier–Stokes equations. The staggered discontinuous Galerkin method is able to preserve the skew-symmetry of the convection term. In addition, by using a local postprocessing technique, the weakly divergence free velocity can be used to compute a new postprocessed velocity, which is exactly divergence free and has a superconvergence property. This strongly divergence free velocity field is the key to the mass conservation. Furthermore, energy stability is improved by the skew-symmetric discretization of the convection term. We will present several numerical results to show the performance of the method.
Journal of Scientific Computing – Springer Journals
Published: Jul 20, 2017
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