We propose a one-parameter family of low-dissipation centred numerical schemes for solving hyperbolic equations in conservative or non-conservative form, using finite volume or discontinuous Galerkin finite element methods. The new schemes spring out from the multi-dimensional FORCE method and are determined by a single parameter α≥1. Given an increasing sequence of real numbers 1≤α₁<α₂<…<α_K, there corresponds a sequence of numerical schemes with stability restriction associated to a decreasing sequence of Courant numbers 1>c₁>c₂>…>c_K>0 and a decreasing sequence of corresponding numerical viscosity functions d₁>d₂>…>d_K. For a given Courant number c_k≤1 there is a real number α_k>0 and a corresponding stable scheme with minimal numerical viscosity d_k. The proposed schemes suit very well the family of high-order discontinuous Galerkin finite element methods and the recently proposed class of ADER-TR schemes, whose orders of accuracy define decreasing sequences of Courant numbers, as the order of accuracy increases. The centred methods of this paper are stable in 2D and 3D in the frame of simultaneous updating formulae, unlike other centred methods, such as 1D FORCE, which are not. Furthermore, the schemes are highly accurate for slowly-moving waves, which is precisely the kind of waves that traditional centred methods smear disastrously. Additional features of the proposed schemes include ease of implementation and applicability to any hyperbolic system either in conservative or non-conservative form. Here, the proposed schemes are analysed and computationally assessed through a suite of test problems for a linear model system, for the Euler equations in one and two space dimensions, and for the Baer-Nunziato equations for compressible two-phase flow.

To study the influence of convective momentum transport (CMT) on wind, boundary layer and cloud evolution in a marine cold air outbreak (CAO) we use large-eddy simulations subject to different baroclinicity (wind shear) but similar surface forcing. The simulated domain is large enough, (Formula presented.) km²), to develop typical mesoscale cellular convective structures. We find that a maximum friction induced by momentum transport (MT) locates in the cloud layer for an increase of geostrophic wind with height (forward shear, FW) and near the surface for a decrease of wind with height (backward shear, BW). Although the total MT always acts as a friction, the interaction of friction-induced cross-isobaric flow with the Coriolis force can develop supergeostrophic winds near the surface (FW) or in the cloud layer (BW). The contribution of convection to MT is evaluated by decomposing the momentum flux by column water vapor and eddy size, revealing that CMT acts to accelerate subcloud layer winds under FW shear and that mesoscale circulations contribute significantly to MT for this horizontal resolution (250 m), even if small-scale eddies are nonnegligible and likely more important as resolution increases. Under FW shear, a deeper boundary layer and faster cloud transition are simulated, because MT acts to increase surface fluxes and wind shear enhances turbulent mixing across cloud tops. Our results show that the coupling between winds and convection is crucial for a range of problems, from CAO lifetime and cloud transitions to ocean heat loss and near-surface wind variability.