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S. Popinet, S. Zaleski (1999)
A front-tracking algorithm for accurate representation of surface tensionInternational Journal for Numerical Methods in Fluids, 30
(2011)
A local discontinuous galerkin method for directly solving HamiltonJacobi equations
R. Gandham, K. Esler, Yongpeng Zhang (2014)
A GPU accelerated aggregation algebraic multigrid methodComput. Math. Appl., 68
J. Grooss, J. Hesthaven (2006)
A level set discontinuous Galerkin method for free surface flowsComputer Methods in Applied Mechanics and Engineering, 195
E. Marchandise, J. Remacle, N. Chevaugeon (2006)
A quadrature-free discontinuous Galerkin method for the level set equationJ. Comput. Phys., 212
(2016)
2016b), “A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin method
E. Marchandise, J. Remacle (2006)
A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flowsJ. Comput. Phys., 219
A. Prosperetti, G. Tryggvason (2007)
Computational Methods for Multiphase Flow: Frontmatter
(2016)
SPHERIC: 3D schematic dam break and evolution of the free surface
M. Owkes, O. Desjardins (2013)
A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flowsJ. Comput. Phys., 249
J. Remacle, N. Chevaugeon, E. Marchandise, C. Geuzaine (2007)
Efficient visualization of high‐order finite elementsInternational Journal for Numerical Methods in Engineering, 69
M. Sussman, M. Hussaini (2003)
A Discontinuous Spectral Element Method for the Level Set EquationJournal of Scientific Computing, 19
Zhihua Xie, D. Pavlidis, J. Percival, J. Gomes, C. Pain, O. Matar (2014)
Adaptive unstructured mesh modelling of multiphase flowsInternational Journal of Multiphase Flow, 67
D. Arnold, F. Brezzi, Bernardo Cockburn, L. Marini (2001)
Unified Analysis of Discontinuous Galerkin Methods for Elliptic ProblemsSIAM J. Numer. Anal., 39
M. Sussman, E. Fatemi (1999)
An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid FlowSIAM J. Sci. Comput., 20
(2005)
Spectral/Hp ElementMethods for CFD
Jue Yan, S. Osher (2011)
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equationsJ. Comput. Phys., 230
E. Lee, D. Violeau, R. Issa, S. Ploix (2010)
Application of weakly compressible and truly incompressible SPH to 3-D water collapse in waterworksJournal of Hydraulic Research, 48
M. Kopera, F. Giraldo (2014)
Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulationsJ. Comput. Phys., 275
C. Hirt, B. Nichols (1981)
Volume of fluid (VOF) method for the dynamics of free boundariesJournal of Computational Physics, 39
M. Sussman, E. Fatemi, S. Osher, P. Smereka (1995)
A level set approach for computing solutions to incompressible two- phase flow II
(1957)
Sur une famille de polynomes ‘a deux variables orthogonaux dans un triangle
M. Sussman, E. Puckett (2000)
A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase FlowsJournal of Computational Physics, 162
E. Puckett, A. Almgren, J. Bell, D. Marcus, W. Rider (1997)
A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible FlowsJournal of Computational Physics, 130
D. Arnold (1982)
An Interior Penalty Finite Element Method with Discontinuous ElementsSIAM Journal on Numerical Analysis, 19
Douglas Enright, Ronald Fedkiw, J. Ferziger, Ian Mitchell (2002)
A hybrid particle level set method for improved interface capturingJournal of Computational Physics, 183
Khosro Shahbazi (2005)
Short Note: An explicit expression for the penalty parameter of the interior penalty methodJournal of Computational Physics, 205
A. Karakus, T. Warburton, M. Aksel, C. Sert (2016)
A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin methodComput. Math. Appl., 72
M. Sussman (2005)
A parallelized, adaptive algorithm for multiphase flows in general geometriesComputers & Structures, 83
M. Sussman, A. Almgren, J. Bell, P. Colella, L. Howell, M. Welcome (1997)
An Adaptive Level Set Approach for Incompressible Two-Phase FlowsJournal of Computational Physics, 148
P. Caron, M. Cruchaga, A. Larreteguy (2015)
Sensitivity analysis of finite volume simulations of a breaking dam problemInternational Journal of Numerical Methods for Heat & Fluid Flow, 25
A. Karakus, Tim Warburton, M. Aksel, C. Sert (2016)
A GPU-accelerated adaptive discontinuous Galerkin method for level set equationInternational Journal of Computational Fluid Dynamics, 30
G. Wu, R. Taylor, D. Greaves (2001)
The effect of viscosity on the transient free-surface waves in a two-dimensional tankJournal of Engineering Mathematics, 40
U. Ozen, TryggvasonGrétar (1992)
A front-tracking method for viscous, incompressible, multi-fluid flowsJournal of Computational Physics
F. Harlow, J. Welch (1965)
Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free SurfacePhysics of Fluids, 8
J. Hesthaven, T. Warburton (2007)
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
J. Guermond, P. Minev, Jie Shen (2006)
An overview of projection methods for incompressible flowsComputer Methods in Applied Mechanics and Engineering, 195
A. Smolianski (2005)
Finite‐element/level‐set/operator‐splitting (FELSOS) approach for computing two‐fluid unsteady flows with free moving interfacesInternational Journal for Numerical Methods in Fluids, 48
G. Tryggvason (1988)
Numerical simulations of the Rayleigh-Taylor instabilityJournal of Computational Physics, 75
T. Koornwinder (1975)
Two-Variable Analogues of the Classical Orthogonal Polynomials
T. Warburton (2007)
An explicit construction of interpolation nodes on the simplexJournal of Engineering Mathematics, 56
(2014)
Adaptive unstructured meshmodelling ofmultiphaseflows
Chung-Yueh Wang, J. Teng, George Huang (2011)
Numerical simulation of sloshing motion inside a two dimensional rectangular tank by level set methodInternational Journal of Numerical Methods for Heat & Fluid Flow, 21
P. Stąpór (2016)
A two-dimensional simulation of solidification processes in materials with thermo-dependent properties using XFEMInternational Journal of Numerical Methods for Heat & Fluid Flow, 26
G. Karniadakis, M. Israeli, S. Orszag (1991)
High-order splitting methods for the incompressible Navier-Stokes equationsJournal of Computational Physics, 97
S. Osher, J. Sethian (1988)
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulationsJournal of Computational Physics, 79
Moshe Dubiner (1991)
Spectral methods on triangles and other domainsJournal of Scientific Computing, 6
David Medina, A. St.-Cyr, T. Warburton (2014)
OCCA: A unified approach to multi-threading languagesArXiv, abs/1403.0968
K. Kleefsman, G. Fekken, A. Veldman, Bogdan Iwanowski, B. Buchner (2005)
A Volume-of-Fluid based simulation method for wave impact problemsJournal of Computational Physics, 206
J. Guermond, L. Quartapelle (2000)
A projection FEM for variable density incompressible flowsJournal of Computational Physics, 165
(2009)
Computational Methods for Multiphase Flow, 1st ed
Yaohong Wang, S. Simakhina, M. Sussman (2012)
A hybrid level set-volume constraint method for incompressible two-phase flowJ. Comput. Phys., 231
This study aims to focus on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation.Design/methodology/approachNodal discontinuous Galerkin discretization is used for incompressible Navier–Stokes, level set advection and reinitialization equations on adaptive unstructured elements. Implicit systems arising from the semi-explicit time discretization of the flow equations are solved with a p-multigrid preconditioned conjugate gradient method, which minimizes the memory requirements and increases overall run-time performance. Computations are localized mostly near the interface location to reduce computational cost without sacrificing the accuracy.FindingsThe proposed method allows to capture interface topology accurately in simulating wide range of flow regimes with high density/viscosity ratios and offers good mass conservation even in relatively coarse grids, while keeping the simplicity of the level set interface modeling. Efficiency, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases of sloshing, dam break and Rayleigh–Taylor instability.Originality/valueA fully discontinuous Galerkin, high-order, adaptive method on unstructured grids is introduced where flow and interface equations are solved in discontinuous space.
International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing
Published: Aug 8, 2018
Keywords: Discontinuous Galerkin; Adaptivity; High-order; Incompressible multiphase flows; Level set; Multigrid
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