A third-order non-oscillatory transport scheme for atmospheric modeling

Atmospheric numerical modeling has been going through drastic changes over the past decade, mainly to utilize the massive computing capability of the petascale systems. This obliges the modelers to develop grid systems and numerical algorithms that facilitate exceptional level of scalability on these systems. The numerical algorithms that can address these challenges should have the local properties such as the high on-processor operation count and minimum parallel communication i.e. high parallel efficiency, it should also satisfy the following properties such as inherent local and global conservation, high-order accuracy, geometric flexibility, non-oscillatory advection, positivity preservation. In the present work, A Third-order Semi-discrete genuinely multidimensional central scheme for systems of conservation laws and related convection-diffusion equations, is considered to address the challenges mentioned above, this scheme is constructed by Kurganov et al. The construction is based on a multidimensional extension of using more precise information of the local speeds of propagation, and integration over non-uniform control volumes, this scheme is a simple genuinely multidimensional semi-discrete scheme. A two-dimensional piecewise quadratic non-oscillatory reconstruction is employed which ensures the high resolution of the scheme. The scheme is demonstrated for different problems in one-dimension, solid-body rotation and deformational flow tests are considered to test the scheme mentioned above in two-dimensions, some accuracy tests were also performed to test the scheme