Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Fast Shallow-Water equation solvers in latitude-longitude coordinates
Journal of Computational Physics
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
A wave propagation method for three-dimensional hyperbolic conservation laws
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Time integration of the shallow water equations in spherical geometry
Journal of Computational Physics
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
A fast solver of the shallow water equations on a sphere using a combined compact difference scheme
Journal of Computational Physics
Wave propagation algorithms on curved manifolds with applications to relativistic hydrodynamics
Wave propagation algorithms on curved manifolds with applications to relativistic hydrodynamics
A wave propagation algorithm for hyperbolic systems on curved manifolds
Journal of Computational Physics
An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
Multiscale simulations for suspensions of rod-like molecules
Journal of Computational Physics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme
Journal of Computational Physics
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 Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
MCore: A non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods
Journal of Computational Physics
A peta-scalable CPU-GPU algorithm for global atmospheric simulations
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
Hermitian Compact Interpolation on the Cubed-Sphere Grid
Journal of Scientific Computing
Hi-index | 31.49 |
Presented in this work is an explicit finite volume method for solving general hyperbolic systems on the surface of a sphere. Applications where such systems arise include passive tracer advection in the atmosphere, shallow water models of the ocean and atmosphere, and shallow water magnetohydrodynamic models of the solar tachocline. The method is based on the curved manifold wave propagation algorithm of Rossmanith, Bale, and LeVeque [A wave propagation algorithm for hyperbolic systems on curved manifolds, J. Comput. Phys. 199 (2004) 631-662], which makes use of parallel transport to approximate geometric source terms and orthonormal Riemann solvers to carry out characteristic decompositions. This approach employs TVD wave limiters, which allows the method to be accurate for both smooth solutions and solutions in which large gradients or discontinuities can occur in the form of material interfaces or shock waves. The numerical grid used in this work is the cubed sphere grid of Ronchi, Iacono, and Paolucci [The 'cubed sphere': a new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys. 124 (1996) 93-114], which covers the sphere with nearly uniform resolution using six identical grid patches with grid lines lying on great circles. Boundary conditions across grid patches are applied either through direct copying from neighboring grid cells in the case of scalar equations or 1D interpolation along great circles in the case of more complicated systems. The resulting numerical method is applied to several test problems for the advection equation, the shallow water equations, and the shallow water magnetohydrodynamic (SMHD) equations. For the SMHD equations, we make use of an unstaggered constrained transport method to maintain a discrete divergence-free magnetic field.