A Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids: Scalar Transport

This is the first paper in a two-part series on the implementation of Godunov-type schemes on unstructured grids for atmospheric flow simulations. Construction of a high-resolution flow solver for the scalar transport equation is described in detail. Higher-order accuracy in space is achieved via a MUSCL-type gradient reconstruction after van Leer and the monotonicity of solution is enforced by slope limiters. Accuracy in time is maintained by implementing a multi-stage explicit Runge-Kutta time-marching algorithm. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. Five different benchmark test cases are simulated for the validation of the numerical scheme.