An Implicit Nonlinearly Consistent Method for the Two-Dimensional Shallow-Water Equations with Coriolis Force

Mousseau, Vincent; Knoll, D. A.; Reisner, Jon

doi:10.1175/1520-0493(2002)130<2611:aincmf>2.0.co;2

Cited by 34 publications

(19 citation statements)

References 31 publications

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“…Although fully implicit methods enjoy an advantage that the time step size is no longer constrained by any stability conditions. If not used properly, the large time step size in a fully implicit method may result in large simulation errors, especially when the dynamical timescale is not properly resolved [22]. In [13], the accuracy of a fully implicit method for a spectral element shallow water code on the cubed-sphere was carefully studied for several test cases and compared with existing fully explicit leapfrog and semi-implicit methods.…”

Section: Introductionmentioning

confidence: 99%

Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere

Yang

Cai

2011

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere

Yang

Cai

2011

Journal of Computational Physics

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“…Although some of them allow substantially larger time steps than a fully explicit scheme, the dependency between the time step length and the horizontal mesh resolution still persists. In addition, due to the inconsistent time integration of different terms in the governing equations, the solution obtained in an operator splitting method may violate the nonlinear consistency which in turn leads to large splitting errors and accuracy degradation [22,29].…”

mentioning

confidence: 99%

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

Yang¹,

Cai²

2014

SIAM J. Sci. Comput.

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Abstract. A fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible Euler equations. To spatially discretize the Euler equations on a height-based terrain-following mesh, we apply a cell-centered finite volume scheme, in which an AUSM + -up method with a piecewise linear reconstruction is employed to achieve secondorder accuracy for the low-Mach flow. A second-order ESDIRK method with adaptive time stepping is applied to stabilize physically insignificant fast waves and accurately integrate the Euler equations in time. The nonlinear system arising at each time step is solved by using a Jacobian-free NewtonKrylov-Schwarz algorithm. To accelerate the convergence and improve the robustness, we employ a class of additive Schwarz preconditioners in which the subdomain Jacobian matrix is constructed using a first-order spatial discretization. Several test cases are used to validate the correctness of the scheme and examine the performance of the solver. Large-scale results on a supercomputer with up to 18, 432 processor cores are provided to show the parallel performance of the proposed method.

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“…Following Mousseau et al 96 , we illustrate the construction of an operatorsplit preconditioner for a sti wave system, speci cally, the one-dimensional shallow water wave equations with a sti gravity w ave:…”

Section: Other Continuation Methods Besides Pseudo-transient Continumentioning

confidence: 99%

Terascale implicit methods for partial differential equations

Keyes¹

2002

Recent Advances in Numerical Methods for Partial Differential Equations and Applications

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An Implicit Nonlinearly Consistent Method for the Two-Dimensional Shallow-Water Equations with Coriolis Force

Cited by 34 publications

References 31 publications

Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere

Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows

Terascale implicit methods for partial differential equations

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