A massively parallel adaptive finite element method with dynamic load balancing
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Spectral transform solutions to the shallow water test set
Journal of Computational Physics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
Spectral/hp methods for viscous compressible flows on unstructured 2D meshes
Journal of Computational Physics
New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
A discontinuous Galerkin method for the viscous MHD equations
Journal of Computational Physics
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
A wave propagation algorithm for hyperbolic systems on curved manifolds
Journal of Computational Physics
Discontinuous Galerkin Methods Applied to Shock and Blast Problems
Journal of Scientific Computing
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Journal of Computational Physics
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
Revisiting the Rossby-Haurwitz wave test case with contour advection
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Dispersion Analysis of Discontinuous Galerkin Schemes Applied to Poincaré, Kelvin and Rossby Waves
Journal of Scientific Computing
Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
Journal of Computational Physics
An edge-based unstructured mesh discretisation in geospherical framework
Journal of Computational Physics
Journal of Computational Physics
A discontinuous/continuous low order finite element shallow water model on the sphere
Journal of Computational Physics
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
Robust untangling of curvilinear meshes
Journal of Computational Physics
Hi-index | 31.48 |
An innovating approach is proposed to solve vectorial conservation laws on curved manifolds using the discontinuous Galerkin method. This new approach combines the advantages of the usual approaches described in the literature. The vectorial fields are expressed in a unit non-orthogonal local tangent basis derived from the polynomial mapping of curvilinear triangle elements, while the convective flux functions are written is the usual 3D Cartesian coordinate system. The number of vectorial components is therefore minimum and the tangency constraint is naturally ensured, while the method remains robust and general since not relying on a particular parametrization of the manifold. The discontinuous Galerkin method is particularly well suited for this approach since there is no continuity requirement between elements for the tangent basis definition. The possible discontinuities of this basis are then taken into account in the Riemann solver on inter-element interfaces. The approach is validated on the sphere, using the shallow water equations for computing standard atmospheric benchmarks. In particular, the Williamson test cases are used to analyze the impact of the geometry on the convergence rates for discretization error. The propagation of gravity waves is eventually computed on non-conventional irregular curved manifolds to illustrate the robustness and generality of the method.