An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

McCorquodale, Peter; Ullrich, P. A.; Johansen, Hans; Colella, Phillip

doi:10.2140/camcos.2015.10.121

Cited by 29 publications

(26 citation statements)

References 59 publications

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“…A detailed description of the model setup to solve the shallow-water equations in conservative flux form can be found in McCorquodale et al (2015). In addition, the Chombo-AMR library is described in Adams et al (2015).…”

Section: Model Descriptionmentioning

confidence: 99%

“…The 2D shallow-water equations serve as a useful test bed for an AMR model as they exhibit many of the complexities present in a full 3D model. We utilize the cubed-sphere fourth-order finite-volume AMR model presented in McCorquodale et al (2015) for the 2D shallow-water equations on the sphere. The model implements a mapped-multiblock AMR technique that overlays refined patches on the coarser grid.…”

Section: Introductionmentioning

confidence: 99%

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Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

Ferguson

Jablonowski

Johansen

et al. 2016

Monthly Weather Review

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Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This paper aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interaction of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse-fine interfaces. Furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.

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Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

Ferguson

Jablonowski

Johansen

et al. 2016

Monthly Weather Review

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“…Least-squares interpolation has also been used at block boundaries for embedded-boundary methods in [20,21] and for high-order coarse-fine mesh interpolation in AMR [25]. The methods of the present paper are applied in [26] to the solution of the shallow-water equations on the surface of a sphere, using AMR.…”

Section: Major Radiusmentioning

confidence: 99%

“…Further work in [26] applies the methods of this paper to the surface of a sphere, which is a 2D manifold in a 3D space, and hence calculations must be consistent with its metric structure. The work in [26] also incorporates adaptive mesh refinement.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

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High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

McCorquodale

Dorr

Hittinger

et al. 2015

Journal of Computational Physics

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We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.

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A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Gao

Owen

Guzik

2016

Numerical Methods in Fluids

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SUMMARYA fourth-order finite-volume method for solving the Navier-Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge-Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.

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An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

Cited by 29 publications

References 59 publications

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

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