A FORWARD-IN-TIME ADVECTION SCHEME AND ADAPTIVE MULTILEVEL FLOW SOLVER FOR NEARLY INCOMPRESSIBLE ATMOSPHERIC FLOW

This paper presents a new forward-in-time advection method for nearly incompressible flow, MU, and its application to an adaptive multilevel flow solver for atmospheric flows. MU is a modification of Leonard et al.'s UTOPIA scheme. MU, like UTOPIA, is based on third-order accurat e semi-Lagrangian multidimensional upwinding for constant velocity flo ws. For varying velocity fields, MU is a second-order conservative met hod. MU has greater stability and accuracy than UTOPIA and naturally d ecomposes into a monotone low-order method and a higher-order accurate correction for use with flux limiting. Its stability and accuracy mak e it a computationally efficient alternative to current finite-differe nce advection methods. We present a fully second-order accurate flow s olver for the anelastic equations, a prototypical low Mach number flow . The flow solver is based on MU which is used for both momentum and s calar transport equations. This flow solver can also be implemented wi th any forward-in-time advection scheme. The multilevel flow solver co nserves discrete global integrals of advected quantities and includes adaptive mesh refinement. Its second-order accuracy is verified using a nonlinear energy conservation integral for the anelastic equations. For a typical geophysical problem in which the flow is most rapidly va rying in a small part of the domain, the multilevel flow solver achiev es global accuracy comparable to a uniform-resolution simulation for 1 0% of the computational cost. (C) 1996 Academic Press. Inc.