High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid.

摘要: High-order numerical methods are applied to the shallow-water equations on sphere. A space-time tensor formalism is used express of motion covariantly and describe geometry rotated cubed-sphere grid. The spatial discretization done with direct flux reconstruction method, which an alternative formulation Discontinuous Galerkin approach. solved in differential form resulting free from quadrature rules. It well known that time step traditional explicit limited by phase speed fastest waves. Exponential integration schemes remove this stability restriction allow larger steps. New multistep exponential propagation iterative orders 4, 5 6 introduced. complex-step approximation Jacobian Krylov-based KIOPS (Krylov incomplete orthogonalization procedure solver) algorithm for computing matrix-vector products {\varphi}-functions. Results evaluated using standard benchmarks.