| A Godunov-type high-resolution scheme based on unstructured meshes for solving the Euler and Navier-Stokes equations governing atmospheric flows is described. The Riemann problem in the Godunov's method is solved using the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. Higher-order spatial accuracy is achieved by gradient reconstruction techniques after van Leer. The total variation diminishing (TVD) condition is enforced with the help of slope limiters. An explicit multi-stage Runge-Kutta time-marching scheme is used to achieve higher-order accuracy in time. The subgrid scale diffusion is based on Smagorinsky's method. The scheme is validated against benchmark cases in one-dimension and idealized test cases in two dimensions. The scheme shows promise in simulating nonhydrostatic atmospheric flows on the meso, micro and urban scale, characterized by steep gradients. |
