Family of spectral filters for discontinuous problems
Journal of Scientific Computing
A spectral element basin model for the shallow water equations
Journal of Computational Physics
Spectral transform solutions to the shallow water test set
Journal of Computational Physics
A parallel hp-adaptive discontinuous Galerkin method for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
SIAM Journal on Scientific Computing
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
SIAM Journal on Scientific Computing
The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
Journal of Computational Physics
Terascale spectral element algorithms and implementations
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
A high-order discontinuous Galerkin method for 2D incompressible flows
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Multiscale Geophysical Modeling Using the Spectral Element Method
Computing in Science and Engineering
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Well balanced finite volume methods for nearly hydrostatic flows
Journal of Computational Physics
Towards an Efficient and Scalable Discontinuous Galerkin Atmospheric Model
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems
Journal of Scientific Computing
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Discontinuous Galerkin spectral/hpelement modelling of dispersive shallow water systems
Journal of Scientific Computing
Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes
Journal of Scientific Computing
Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations
Journal of Computational Physics
Journal of Computational Physics
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
Idempotent filtering in spectral and spectral element methods
Journal of Computational Physics
Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators
Computers & Mathematics with Applications
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
A Parallel High-Order Discontinuous Galerkin Shallow Water Model
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
A Fully Implicit Jacobian-Free High-Order Discontinuous Galerkin Mesoscale Flow Solver
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Journal of Computational Physics
Journal of Computational Physics
High-order finite-volume methods for the shallow-water equations on the sphere
Journal of Computational Physics
Journal of Scientific Computing
Structural Stability of Discontinuous Galerkin Schemes
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Journal of Computational Physics
Journal of Computational Physics
A New Class of High-Order Energy Stable Flux Reconstruction Schemes
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Nonlinear OIFS for a hybrid galerkin atmospheric model
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
A discontinuous/continuous low order finite element shallow water model on the sphere
Journal of Computational Physics
High-Order finite element methods for parallel atmospheric modeling
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
On the accuracy of high-order finite elements in curvilinear coordinates
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Journal of Computational Physics
Journal of Computational Physics
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.57 |
We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface. The global solutions are represented by a collection of curvilinear quadrilaterals from an icosahedral grid. On each of these elements the local solutions are assumed to be well approximated by a high-order nodal Lagrange polynomial, constructed from a tensor-product of the Legendre-Gauss-Lobatto points, which also supplies a high-order quadrature. The shallow water equations are satisfied in a local discontinuous element fashion with solution continuity being enforced weakly. The numerical experiments, involving a comparison of weak and strong conservation forms and the impact of over-integration and filtering, confirm the expected high-order accuracy and the potential for using such highly parallel formulations in numerical weather prediction.