A Forward-in-time Advection Scheme and Adaptive Multilevel Ow Solver for Nearly Incompressible Atmospheric Ow Running Head: Adaptive Multilevel Solver for Atmospheric Ow Corresponding Author Address

This paper presents a new forward-in-time advection method for nearly incompressible ow, MU, and its application to an adaptive multilevel ow solver for atmospheric ows. MU is a modi cation of Leonard et al.'s (1993) UTOPIA scheme. MU, like UTOPIA, is based on third-order accurate semiLagrangian multidimensional upwinding for constant velocity ows. For varying velocity elds, MU is a second-order conservative method. MU has greater stability and accuracy than UTOPIA, and naturally decomposes into a monotone low-order method and a higher-order accurate correction for use with ux limiting. Its stability and accuracy make it a computationally e cient alternative to current nite-di erence advection methods. We present a fully second-order accurate ow solver for the anelastic equations, a prototypical low Mach number ow. The ow solver is based on MU which is used for both momentum and scalar transport equations. This ow solver can also be implemented with any forward-in-time advection scheme. The multilevel ow solver conserves discrete global integrals of advected quantities, and includes adaptive mesh re nement. Its second-order accuracy is veri ed using a nonlinear energy conservation integral for the aneleastic equations. For a typical geophysical problem in which the ow is most rapidly varying in a small part of the domain, the multilevel ow solver achieves global accuracy comparable to a uniformresolution simulation for 10% of the computational cost.