Twenty years ago, the multidimensional, positive de nite, advection transport algorithm was introduced by Smolarkiewicz. Over the two decades since, it has been applied countless times to numerous problems, however almost always on rectilinear grids. One of the few exceptions is the Operational Multiscale Environment model with Grid Adaptivity (OMEGA), an atmospheric simulation system originall...

Advection schemes with time step restrictions are widely used in weather and climate models. This can lead to instability the presence of high flow speeds (relative mesh spacing) such as occurs convective updraughts, regions convergence, or where winds unusually high. An adaptively implicit advection scheme is proposed that treats implicitly only Courant number Flux correction ensure monotonici...

We present a new finite difference code for modeling three-dimensional thermal convection in a spherical shell using the “cubed sphere” method of Ronchi et al. [1]. The equation of motion is solved using a poloidal potential formulation for an iso-viscous, infinite Prandtl number fluid on a finite difference grid and advective transport is implemented using the 2nd-order MPDATA scheme of Smolar...

A three-dimensional semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic anelastic equations, suitable for simulation of small-to-mesoscale atmospheric flows. The model builds on nonoscillatory forwardin-time MPDATA approach using finite-volume discretization and admitting unstructured meshes with arbitrarily shaped cells. The numerical advancements are e...

Three object-oriented implementations of a prototype solver of the advection equation are introduced. The presented programs are based on Blitz++ (C++), NumPy (Python), and Fortran’s built-in array containers. The solvers include an implementation of the Multidimensional Positive-Definite Advective Transport Algorithm (MPDATA). The introduced codes exemplify how the application of object-orient...

Abstract. This work discusses the numerical aspects of representing condensational growth particles in models aerosol systems such as atmospheric clouds. It focuses on Eulerian modelling approach, which fixed-bin discretisation is used for probability density function describing particle-size spectrum. Numerical diffusion inherent to employment solving arising transport problem (advection equat...

We present a novel approach for numerical simulation of uid ow and sediment transport past evolutionary landforms, with emphasis on sand dunes developing in extreme winds. Time-dependent curvilinear coordinates are employed to fully couple ow aloft with the developing landform. The conservation law that de nes shape of the lower boundary depends on details of local surface stress, thereby favou...