Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
A Bi-Hyperbolic Finite Volume Method on Quadrilateral Meshes
Journal of Scientific Computing
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
SIAM Journal on Numerical Analysis
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
High Order Extensions of Roe Schemes for Two-Dimensional Nonconservative Hyperbolic Systems
Journal of Scientific Computing
Simulation of shallow-water systems using graphics processing units
Mathematics and Computers in Simulation
An MPI-CUDA implementation of an improved Roe method for two-layer shallow water systems
Journal of Parallel and Distributed Computing
Parallelization of shallow water simulations on current multi-threaded systems
International Journal of High Performance Computing Applications
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We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J. Sci. Comput. 39:67---114, 2009) for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.