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A Lagrangian staggered grid Godunov-like approach for hydrodynamics

Nathaniel R. Morgan, Konstantin N. Lipnikov, Donald E. Burton, Mark A. Kenamond
2014 Journal of Computational Physics  
Much research in Lagrangian staggered-grid hydrodynamics (SGH) has focused on explicit viscosity models for adding dissipation to a calculation that has shocks.  ...  This approach adds dissipation to the calculation via solving a Riemann-like problem.  ...  We are grateful for the help of Scott Ramsey on the Kidder problem. We also thank Misha Shashkov for his input on this research effort. The Los Alamos unlimited release number is: LA-UR-13-23442.  ... 
doi:10.1016/j.jcp.2013.12.013 fatcat:rn2t3sgnarbddft7besdoawg2e

Page 1806 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations.  ...  We develop both second- and fourth-order finite difference methods on a staggered grid, together with a fully implicit time-marching scheme, using grid generation to accommodate fairly general geometries  ... 

3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity

Raphaël Loubère, Pierre-Henri Maire, Pavel Váchal
2012 International Journal for Numerical Methods in Fluids  
The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids.  ...  A 3D version of such schemes has been presented for instance in [15] [16] [17] . In [1], the authors derived a staggered discretization for 2D Lagrangian hydrodynamics on unstructured grids.  ...  The authors would like to acknowledge the support of the French embassy in Prague, Czech Republic, under the Vltava program; it provided the conditions for this work to reach maturity.  ... 
doi:10.1002/fld.3730 fatcat:im7lv3qonnhuzmxl2om3atotvy

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Raphaël Loubère, Pierre-Henri Maire, Mikhail Shashkov, Jérôme Breil, Stéphane Galera
2010 Journal of Computational Physics  
The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which  ...  We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method.  ...  In this paper the author proposed a new formulation of continuum hydrodynamics based on an unstructured grid.  ... 
doi:10.1016/j.jcp.2010.03.011 fatcat:okk7wpwtcrhmzdfweha3dwdl2u

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

Nathaniel R. Morgan, Jacob I. Waltz, Donald E. Burton, Marc R. Charest, Thomas R. Canfield, John G. Wohlbier
2015 Journal of Computational Physics  
A challenge, however, is tetrahedron meshes do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme  ...  The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach.  ...  Acknowledgements We would like to thank L. Dean Risinger for developing data structures for unstructured tetrahedron meshes.  ... 
doi:10.1016/j.jcp.2014.10.048 fatcat:5wbqhxmhebbgheqt5n2aq6u67a

Multidimensional staggered grid residual distribution scheme for Lagrangian hydrodynamics [article]

R. Abgrall, K. Lipnikov, N. Morgan, S. Tokareva
2018 arXiv   pre-print
We present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics.  ...  Thanks to the generic formulation of the staggered grid residual distribution scheme, it can be directly applied to both single- and multimaterial and multiphase models.  ...  A. Kenamond, A Lagrangian staggered grid Godunov-like approach for hydrodynamics, J. Comput. Phys., 259 (2014), pp. 568–597. [27] W. F.  ... 
arXiv:1811.00057v1 fatcat:trpq6thifnfjxmthao6244w474

Arbitrary-Lagrangian–Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Walter Boscheri, Michael Dumbser
2017 Journal of Computational Physics  
is achieved by the ADER approach.  ...  We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple  ...  Nkonga, Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics, J. Comput. Phys. 228 (2009) 799–821. [100] A. Meister, S.  ... 
doi:10.1016/j.jcp.2017.06.022 fatcat:wzwrxo5ufjhavamb3txl23i4we

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

François Vilar, Chi-Wang Shu, Pierre-Henri Maire
2016 Journal of Computational Physics  
This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation.  ...  After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume  ...  The staggered hydrodynamics has been developed to avoid such complications.  ... 
doi:10.1016/j.jcp.2016.02.027 fatcat:mo55not735elhk5stuspbowata

A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes

Pierre-Henri Maire
2009 Journal of Computational Physics  
We note also the recent development of a variational multi-scale stabilized approach in finite element computation of Lagrangian hydrodynamics, where a piecewise linear approximation was adopted for the  ...  This drawback is critical for real-life Lagrangian computations in which the grid often contains high aspect ratio cells.  ...  Nkonga for his interest and many fruitful discussions.  ... 
doi:10.1016/j.jcp.2008.12.007 fatcat:h6xevxf5svgfnjzf6ed75xoyte

A second-order cell-centered Lagrangian scheme for two-dimensional compressible flow problems

Pierre-Henri Maire, Jérôme Breil
2008 International Journal for Numerical Methods in Fluids  
We note also the recent development of a variational multi-scale stabilized approach in finite element computation of Lagrangian hydrodynamics, where a piecewise linear approximation was adopted for the  ...  This drawback is critical for real-life Lagrangian computations in which the grid often contains high aspect ratio cells.  ...  Nkonga for his interest and many fruitful discussions.  ... 
doi:10.1002/fld.1564 fatcat:vy5p5irsnzcgjb5q7juldi422e

The numerical simulation of two-dimensional fluid flow with strong shocks

Paul Woodward, Phillip Colella
1984 Journal of Computational Physics  
Results of an extensive comparison of numerical methods for simulating hydrodynamics are presented and discussed.  ...  The advantages and disadvantages of each approach are discussed and illustrated by computed results for three test problems.  ...  We would particularly like to acknowledge the enlightening discussions we have had with Drs. S. Zalesak and B. van Leer. This work was performed in part under the auspices of the U.S.  ... 
doi:10.1016/0021-9991(84)90142-6 fatcat:g5amuigjwnazbef66cmszaweim

Current Advances in the Methodology and Computational Simulation of the Formation of Low-Mass Stars [article]

Richard I. Klein, Shu-ichiro Inutsuka, Paolo Padoan, Kohji Tomisaka
2006 arXiv   pre-print
challenge for simulations.  ...  Among such techniques, Adaptive Mesh Refinement and Smooth Particle Hydrodynamics have provided frameworks to simulate the process of low-mass star formation with a very large dynamic range.  ...  Approaches for Magneto-Hydrodynamics Since strong shocks often appear in the astrophysical phenomena, a shock-capturing scheme is needed also in MHD.  ... 
arXiv:astro-ph/0603711v1 fatcat:nhsdyw2bdnhujmtnwyrihq6lka

A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics

Andrew L. Zachary, Andrea Malagoli, Phillip Colella
1994 SIAM Journal on Scientific Computing  
The authors present a higher-order Godunov method for the solution of the two-and three-dimensional equations of ideal magnetohydrodynamics (MHD).  ...  In this paper, we present a new, multidimensional scheme for the equations of ideal MHD, which is based on a higher-order Godunov method specially developed to treat the degeneracies that occur in these  ...  Spicer and the staff of the NASA Center for Computational Sciences (NCCS) for providing the supercomputing resources.  ... 
doi:10.1137/0915019 fatcat:g4zyydcryjdurguhcu6rdnil4u

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

Nathaniel R. Morgan, Jacob I. Waltz, Donald E. Burton, Marc R. Charest, Thomas R. Canfield, John G. Wohlbier
2015 Journal of Computational Physics  
We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes.  ...  All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron.  ...  Acknowledgements We would like to thank L. Dean Risinger for developing data structures for unstructured tetrahedral meshes. We are grateful for the help from Scott Ramsey on the Kidder problems.  ... 
doi:10.1016/j.jcp.2015.02.024 fatcat:bkpmbkoisvavbe6vfniiyufny4

Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

Pierre-Henri Maire, Boniface Nkonga
2009 Journal of Computational Physics  
This work presents a multidimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism.  ...  The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm. P n+1 c = P (ρ n+1 c , ε n+1 c ).  ...  At the discrete level, the most natural framework employs staggered-grid hydrodynamics (SGH).  ... 
doi:10.1016/j.jcp.2008.10.012 fatcat:wmm6daehtjg47mayulmmxf6nwu
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