Spherical perfect lens: Solutions of Maxwell’s equations for spherical geometry

Spectral Viscosity for Shallow Water Equations in Spherical Geometry

A spherical spectral viscosity operator is proposed as an alternative to standard horizontal diffusion terms in global atmospheric models. Implementation in NCAR’s Spectral Transform Shallow Water Model and application to a suite of standard test cases demonstrates improvement in resolution and numerical conservation of invariants at no extra computational cost. The retention in the spectral vi...

Approximate Solutions of Equations Defined by Complex Spherical Multiplier Operators

Exact Solutions of Compressible Flow Equations with Spherical Symmetry

In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [1], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of mo...

Analytical solutions of the simplified spherical harmonics equations.

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared t...

Hexagonal Geometry Clipmaps for Spherical Terrain Rendering

Terrains can be rendered efficiently with rectangular 2D grid of heights. Terrain on spheres, on the other hand, can be rendered using Hierarchical Triangular Mesh (HTM) but the representation does not fit directly with 2D grid of heights. We present a unified representation of HTM and clipmapping using Hexagonal Geometry Clipmaps. This provides one to one correspondence of vertices and heights...