Journal of Computational Physics
The multidimensional positive definite advection transport algorithm: nonoscillatory option
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
An optimization of the Icosahedral grid modified by spring dynamics
Journal of Computational Physics
MPDATA: An edge-based unstructured-grid formulation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
An edge-based unstructured mesh discretisation in geospherical framework
Journal of Computational Physics
Journal of Computational Physics
Method of Moving Frames to Solve Conservation Laws on Curved Surfaces
Journal of Scientific Computing
A class of semi-implicit predictor-corrector schemes for the time integration of atmospheric models
Journal of Computational Physics
Computers & Mathematics with Applications
Hi-index | 31.47 |
A finite volume algorithm for the solution of the reaction-advection-diffusion equation on the sphere is derived and evaluated using analytical solutions. The proposed approach is based on the principle of semidiscretization. The convective and diffusive fluxes are approximated first, and then the resulting set of the ordinary differential equations (ODEs) is solved using the appropriate time stepping algorithm. In the first part of the paper, solutions to both the linear advection and the advection-diffusion problems for a single conservative scalar are discussed. The monotonicity of the scheme is achieved with the explicit adaptive dissipation. The development as well as the selected applications of the method are illustrated using a finite volume mesh constructed on the basis of geodesic icosahedral grid, which, in the past 40 years, has been frequently applied in different models of geophysical fluid dynamics. The performance of the solver is assessed using a suite of standard tests based on solid body rotation for different initial conditions. After analysis of the advection-diffusion problem, the extension of the method for the equations with reactive terms is presented. The performance of the solver is assessed by comparing the results to the analytical solution of the linearized reaction-diffusion system. In the final part of the paper, the application of the solver for studies of nonlinear reactions on the sphere is illustrated. The main intended application of the proposed method includes the simulation of transport of chemical constituents in the Earth's atmosphere as well as the forecasting of moisture and cloud water fields in numerical weather prediction and climate models.