Multidimensional method-of-lines transport for atmospheric flows over steep terrain using arbitrary meshes

摘要

Including terrain in atmospheric models gives rise to mesh distortions nearthe lower boundary that can degrade accuracy and challenge the stability oftransport schemes. Multidimensional transport schemes avoid splitting errors ondistorted, arbitrary meshes, and method-of-lines schemes have low computationalcost because they perform reconstructions at fixed points. This paper presents a multidimensional method-of-lines finite volumetransport scheme, "cubicFit", which is designed to be numerically stable onarbitrary meshes. Stability conditions derived from a von Neumann stabilityanalysis are imposed during model initialisation to obtain stability andimprove accuracy in distorted regions of the mesh, and near steeply-slopinglower boundaries. Reconstruction calculations depend upon the mesh only,needing just one vector multiply per face per time-stage irrespective of thevelocity field. The cubicFit scheme is evaluated using three, idealised numerical tests. Thefirst is a variant of a standard horizontal transport test on severelydistorted terrain-following meshes. The second is a new test case that assessesaccuracy near the ground by transporting a tracer at the lower boundary oversteep terrain on terrain-following meshes, cut-cell meshes, and new,slanted-cell meshes that do not suffer from severe time-step constraintsassociated with cut cells. The third, standard test deforms a tracer in avortical flow on hexagonal-icosahedral meshes and cubed-sphere meshes. In alltests, cubicFit is stable and largely insensitive to mesh distortions, andcubicFit results are more accurate than those obtained using a multidimensionallinear upwind transport scheme. The cubicFit scheme is second-order convergentregardless of mesh distortions.