A high resolution numerical method for solving atmospheric models

We develop a numerical method to solve atmospheric model equations, which is a hybrid of the exponential time differencing (ETD) and the equation solving solution gradient (ESSG) method. The Coriolis force term due to geostrophic effects is handled by the ETD method and the convective flux balance terms are implemented by the ESSG method. In the ESSG method, gradients of solution variables are solved by their corresponding difference equations instead of interpolating from nearby solution values as in the conventional finite volume method. In this way, significant features of the model equations can be preserved and correctly considered to provide a reliable simulation. Feasibility of the proposed method is verified in a number of applications and shows it is more accurate than other common schemes, including the first-order upwind (UD) scheme and the second-order minimum modulus (minmod) scheme. We apply the method to a one-dimensional shock tube, a two-dimensional Riemann problem, and an atmospheric vortex flow. Our studies indicate that the exponential time differencing together with the equation solving solution gradient method provides very accurate simulations for the atmospheric flow model equations.