A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport.
Castro-Díaz, M. J.; Fernández-Nieto, E. D.; Morales de Luna, T.; Narbona-Reina, G.; and Parés, C.
ESAIM: Mathematical Modelling and Numerical Analysis, 47(1): 1-32. 7 2012.
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@article{CastroDiaz2012,
abstract = {The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity preserving property of the corresponding numerical methods are presented. The numerical results provided by the two HLLC solvers are compared between them and also with those obtained with a Roe-type method in a number of 1d and 2d test problems. This comparison shows that, while the quality of the numerical solutions is comparable, the computational cost of the HLLC solvers is lower, as only some partial information of the eigenstructure of the matrix system is needed.},
author = {Castro-D\'iaz, M. J., Fern\'andez-Nieto, E. D. , Morales de Luna, Tom�s, Narbona-Reina, G.., Par\'es, Carlos},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Well-balanced; finite volume method; path-conservative; simple Riemann solver; HLLC; well-balanced},
language = {eng},
month = {7},
number = {1},
doi = {http://dx.doi.org/10.1051/m2an/2012017},
pages = {1-32},
publisher = {EDP Sciences},
title = {A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport},
volume = {47},
year = {2012},
url_Paper = {http://hdl.handle.net/11441/31922},
}
The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity preserving property of the corresponding numerical methods are presented. The numerical results provided by the two HLLC solvers are compared between them and also with those obtained with a Roe-type method in a number of 1d and 2d test problems. This comparison shows that, while the quality of the numerical solutions is comparable, the computational cost of the HLLC solvers is lower, as only some partial information of the eigenstructure of the matrix system is needed.
A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods.
Castro-Díaz, M. J.; and Fernández-Nieto, E. D.
SIAM Journal on Scientific Computing, 34(4): A2173-A2196. 2012.
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@article{doi101137/100795280,
author = {Castro-D\'iaz, M. J. and Fern\'andez-Nieto, E. D. },
title = {A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods},
journal = {SIAM Journal on Scientific Computing},
volume = {34},
url_Paper = {http://hdl.handle.net/11441/32926},
number = {4},
pages = {A2173-A2196},
year = {2012},
doi = {10.1137/100795280},
eprint = {
https://doi.org/10.1137/100795280
}
}
A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model.
Acary-Robert, C.; Fernández-Nieto, E. D.; Narbona-Reina, G.; and Vigneaux, P.
Journal of Scientific Computing, 53(3): 608-641. April 2012.
40 pages. 12 figures.
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@article{acaryroberthal00709491,
TITLE = {{A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model}},
AUTHOR = {Acary-Robert, C. and Fern\'andez-Nieto, E. D. and Narbona-Reina, G.. and Vigneaux, Paul},
NOTE = {40 pages. 12 figures.},
JOURNAL = {{Journal of Scientific Computing}},
PUBLISHER = {{Springer Verlag}},
VOLUME = {53},
NUMBER = {3},
PAGES = {608-641},
YEAR = {2012},
MONTH = Apr,
DOI = {10.1007/s10915-012-9591-x},
KEYWORDS = {variational inequality ; finite volume ; well balanced ; Herschel-Bulkley ; viscous shallow water ; avalanche},
HAL_ID = {hal-00709491},
HAL_VERSION = {v1},
url_Paper = {http://hdl.handle.net/11441/32223},
}
An MPI-CUDA implementation of an improved Roe method for two-layer shallow water systems.
de la Asunción, M.; Mantas, J. M.; Castro-Díaz, M. J.; and Fernández-Nieto, E. D.
Journal of Parallel and Distributed Computing, 72(9): 1065-1072. 2012.
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abstract
@article{jpdc2012,
author = {de la Asunci\'on, Marc and Jos\'e M. Mantas and Castro-D\'iaz, M. J. and Fern\'andez-Nieto, E. D. },
abstract = {The numerical solution of two-layer shallow water systems is required to simulate accurately stratified fluids, which are ubiquitous in nature: they appear in atmospheric flows, ocean currents, oil spills, etc. Moreover, the implementation of the numerical schemes to solve these models in realistic scenarios imposes huge demands of computing power. In this paper, we tackle the acceleration of these simulations in triangular meshes by exploiting the combined power of several CUDA-enabled GPUs in a GPU cluster. For that purpose, an improvement of a path conservative Roe-type finite volume scheme which is specially suitable for GPU implementation is presented, and a distributed implementation of this scheme which uses CUDA and MPI to exploit the potential of a GPU cluster is developed. This implementation overlaps MPI communication with CPU�GPU memory transfers and GPU computation to increase efficiency. Several numerical experiments, performed on a cluster of modern CUDA-enabled GPUs, show the efficiency of the distributed solver.},
journal = {Journal of Parallel and Distributed Computing},
number = {9},
pages = {1065-1072},
title = {{A}n {MPI}-{CUDA} implementation of an improved {R}oe method for two-layer shallow water systems},
volume = {72},
year = {2012},
doi = {http://dx.doi.org/10.1016/j.jpdc.2011.07.012},
url_Paper = {http://hdl.handle.net/11441/32925},
}
The numerical solution of two-layer shallow water systems is required to simulate accurately stratified fluids, which are ubiquitous in nature: they appear in atmospheric flows, ocean currents, oil spills, etc. Moreover, the implementation of the numerical schemes to solve these models in realistic scenarios imposes huge demands of computing power. In this paper, we tackle the acceleration of these simulations in triangular meshes by exploiting the combined power of several CUDA-enabled GPUs in a GPU cluster. For that purpose, an improvement of a path conservative Roe-type finite volume scheme which is specially suitable for GPU implementation is presented, and a distributed implementation of this scheme which uses CUDA and MPI to exploit the potential of a GPU cluster is developed. This implementation overlaps MPI communication with CPU�GPU memory transfers and GPU computation to increase efficiency. Several numerical experiments, performed on a cluster of modern CUDA-enabled GPUs, show the efficiency of the distributed solver.
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